[{"data":1,"prerenderedAt":3837},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Farithmetic\u002Frentenendwert":546,"formula-related-de\u002Fformulas\u002Fmath\u002Farithmetic\u002Frentenendwert":3824},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":556,"category":65,"checks":3762,"conditions":3781,"conditionsHtml":3782,"deprecated":3783,"description":3755,"extension":3784,"figure":3783,"figureCaption":3783,"figureHtml":3783,"formulaId":3785,"latex":3786,"latexHtml":3787,"level":3788,"meta":3789,"navigation":3790,"path":3791,"redirectFrom":3792,"related":3793,"seo":3798,"stem":3799,"subject":583,"summary":3800,"tags":3801,"variables":3807,"__hash__":3823},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Farithmetic\u002Frentenendwert.md","Rentenendwert",[550,551,552,553,554,555],"Sparplan berechnen","Endwert einer Rente","regelmäßig sparen mit Zinsen","nachschüssige Rente","vorschüssige Rente","Rentenendwertformel",{"type":557,"value":558,"toc":3754},"minimark",[559,564,720,731,1060,1233,1237,1346,1864,1868,1977,2302,2706,2861,3348,3352],[560,561,563],"h2",{"id":562},"erklärung","Erklärung",[565,566,567,568,572,573,620,621,624,625,627,628,719],"p",{},"Bei einem ",[569,570,571],"strong",{},"Sparplan"," zahlt man regelmäßig denselben Betrag ",[574,575,578,600],"span",{"className":576},[577],"katex",[574,579,582],{"className":580},[581],"katex-mathml",[583,584,586],"math",{"xmlns":585},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[587,588,589,596],"semantics",{},[590,591,592],"mrow",{},[593,594,595],"mi",{},"r",[597,598,595],"annotation",{"encoding":599},"application\u002Fx-tex",[574,601,605],{"className":602,"ariaHidden":604},[603],"katex-html","true",[574,606,609,614],{"className":607},[608],"base",[574,610],{"className":611,"style":613},[612],"strut","height:0.4306em;",[574,615,595],{"className":616,"style":619},[617,618],"mord","mathnormal","margin-right:0.0278em;"," ein, die ",[569,622,623],{},"Rate",". Jede Rate wird verzinst, aber unterschiedlich lange: Die erste Rate liegt am längsten auf dem Konto, die letzte gar nicht. Der ",[569,626,548],{}," ",[574,629,631,652],{"className":630},[577],[574,632,634],{"className":633},[581],[583,635,636],{"xmlns":585},[587,637,638,649],{},[590,639,640],{},[641,642,643,646],"msub",{},[593,644,645],{},"R",[593,647,648],{},"n",[597,650,651],{"encoding":599},"R_n",[574,653,655],{"className":654,"ariaHidden":604},[603],[574,656,658,662],{"className":657},[608],[574,659],{"className":660,"style":661},[612],"height:0.8333em;vertical-align:-0.15em;",[574,663,665,669],{"className":664},[617],[574,666,645],{"className":667,"style":668},[617,618],"margin-right:0.0077em;",[574,670,673],{"className":671},[672],"msupsub",[574,674,678,710],{"className":675},[676,677],"vlist-t","vlist-t2",[574,679,682,705],{"className":680},[681],"vlist-r",[574,683,687],{"className":684,"style":686},[685],"vlist","height:0.1514em;",[574,688,690,695],{"style":689},"top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;",[574,691],{"className":692,"style":694},[693],"pstrut","height:2.7em;",[574,696,702],{"className":697},[698,699,700,701],"sizing","reset-size6","size3","mtight",[574,703,648],{"className":704},[617,618,701],[574,706,709],{"className":707},[708],"vlist-s","​",[574,711,713],{"className":712},[681],[574,714,717],{"className":715,"style":716},[685],"height:0.15em;",[574,718],{}," ist das gesamte Guthaben am Ende.",[565,721,722,723,726,727,730],{},"Die Formel gilt für ",[569,724,725],{},"nachschüssige"," Raten, die jeweils am Jahresende eingezahlt werden. Bei ",[569,728,729],{},"vorschüssigen"," Raten am Jahresanfang wird jede Rate ein Jahr länger verzinst:",[574,732,735],{"className":733},[734],"katex-display",[574,736,738,803],{"className":737},[577],[574,739,741],{"className":740},[581],[583,742,744],{"xmlns":585,"display":743},"block",[587,745,746,800],{},[590,747,748,759,763,765,768,771,773],{},[749,750,751,753,755],"msubsup",{},[593,752,645],{},[593,754,648],{},[756,757,758],"mtext",{},"vor",[760,761,762],"mo",{},"=",[593,764,595],{},[760,766,767],{},"⋅",[593,769,770],{},"q",[760,772,767],{},[774,775,776,792],"mfrac",{},[590,777,778,785,788],{},[779,780,781,783],"msup",{},[593,782,770],{},[593,784,648],{},[760,786,787],{},"−",[789,790,791],"mn",{},"1",[590,793,794,796,798],{},[593,795,770],{},[760,797,787],{},[789,799,791],{},[597,801,802],{"encoding":599},"R_n^{\\text{vor}} = r \\cdot q \\cdot \\frac{q^n - 1}{q - 1}",[574,804,806,887,908,928],{"className":805,"ariaHidden":604},[603],[574,807,809,813,875,880,884],{"className":808},[608],[574,810],{"className":811,"style":812},[612],"height:0.9614em;vertical-align:-0.247em;",[574,814,816,819],{"className":815},[617],[574,817,645],{"className":818,"style":668},[617,618],[574,820,822],{"className":821},[672],[574,823,825,866],{"className":824},[676,677],[574,826,828,863],{"className":827},[681],[574,829,832,844],{"className":830,"style":831},[685],"height:0.7144em;",[574,833,835,838],{"style":834},"top:-2.453em;margin-left:-0.0077em;margin-right:0.05em;",[574,836],{"className":837,"style":694},[693],[574,839,841],{"className":840},[698,699,700,701],[574,842,648],{"className":843},[617,618,701],[574,845,847,850],{"style":846},"top:-3.113em;margin-right:0.05em;",[574,848],{"className":849,"style":694},[693],[574,851,853],{"className":852},[698,699,700,701],[574,854,856],{"className":855},[617,701],[574,857,860],{"className":858},[617,859,701],"text",[574,861,758],{"className":862},[617,701],[574,864,709],{"className":865},[708],[574,867,869],{"className":868},[681],[574,870,873],{"className":871,"style":872},[685],"height:0.247em;",[574,874],{},[574,876],{"className":877,"style":879},[878],"mspace","margin-right:0.2778em;",[574,881,762],{"className":882},[883],"mrel",[574,885],{"className":886,"style":879},[878],[574,888,890,894,897,901,905],{"className":889},[608],[574,891],{"className":892,"style":893},[612],"height:0.4445em;",[574,895,595],{"className":896,"style":619},[617,618],[574,898],{"className":899,"style":900},[878],"margin-right:0.2222em;",[574,902,767],{"className":903},[904],"mbin",[574,906],{"className":907,"style":900},[878],[574,909,911,915,919,922,925],{"className":910},[608],[574,912],{"className":913,"style":914},[612],"height:0.6389em;vertical-align:-0.1944em;",[574,916,770],{"className":917,"style":918},[617,618],"margin-right:0.0359em;",[574,920],{"className":921,"style":900},[878],[574,923,767],{"className":924},[904],[574,926],{"className":927,"style":900},[878],[574,929,931,935],{"className":930},[608],[574,932],{"className":933,"style":934},[612],"height:2.2218em;vertical-align:-0.8804em;",[574,936,938,943,1056],{"className":937},[617],[574,939],{"className":940},[941,942],"mopen","nulldelimiter",[574,944,946],{"className":945},[774],[574,947,949,1047],{"className":948},[676,677],[574,950,952,1044],{"className":951},[681],[574,953,956,981,992],{"className":954,"style":955},[685],"height:1.3414em;",[574,957,959,963],{"style":958},"top:-2.314em;",[574,960],{"className":961,"style":962},[693],"height:3em;",[574,964,966,969,972,975,978],{"className":965},[617],[574,967,770],{"className":968,"style":918},[617,618],[574,970],{"className":971,"style":900},[878],[574,973,787],{"className":974},[904],[574,976],{"className":977,"style":900},[878],[574,979,791],{"className":980},[617],[574,982,984,987],{"style":983},"top:-3.23em;",[574,985],{"className":986,"style":962},[693],[574,988],{"className":989,"style":991},[990],"frac-line","border-bottom-width:0.04em;",[574,993,995,998],{"style":994},"top:-3.677em;",[574,996],{"className":997,"style":962},[693],[574,999,1001,1032,1035,1038,1041],{"className":1000},[617],[574,1002,1004,1007],{"className":1003},[617],[574,1005,770],{"className":1006,"style":918},[617,618],[574,1008,1010],{"className":1009},[672],[574,1011,1013],{"className":1012},[676],[574,1014,1016],{"className":1015},[681],[574,1017,1020],{"className":1018,"style":1019},[685],"height:0.6644em;",[574,1021,1023,1026],{"style":1022},"top:-3.063em;margin-right:0.05em;",[574,1024],{"className":1025,"style":694},[693],[574,1027,1029],{"className":1028},[698,699,700,701],[574,1030,648],{"className":1031},[617,618,701],[574,1033],{"className":1034,"style":900},[878],[574,1036,787],{"className":1037},[904],[574,1039],{"className":1040,"style":900},[878],[574,1042,791],{"className":1043},[617],[574,1045,709],{"className":1046},[708],[574,1048,1050],{"className":1049},[681],[574,1051,1054],{"className":1052,"style":1053},[685],"height:0.8804em;",[574,1055],{},[574,1057],{"className":1058},[1059,942],"mclose",[565,1061,1062,1063,1117,1118,1232],{},"Zinssatz und Zahlungsabstand müssen zusammenpassen; die Formel hier gilt für jährliche Raten mit Jahreszins. Für ",[574,1064,1066,1085],{"className":1065},[577],[574,1067,1069],{"className":1068},[581],[583,1070,1071],{"xmlns":585},[587,1072,1073,1082],{},[590,1074,1075,1077,1079],{},[593,1076,565],{},[760,1078,762],{},[789,1080,1081],{},"0",[597,1083,1084],{"encoding":599},"p = 0",[574,1086,1088,1107],{"className":1087,"ariaHidden":604},[603],[574,1089,1091,1095,1098,1101,1104],{"className":1090},[608],[574,1092],{"className":1093,"style":1094},[612],"height:0.625em;vertical-align:-0.1944em;",[574,1096,565],{"className":1097},[617,618],[574,1099],{"className":1100,"style":879},[878],[574,1102,762],{"className":1103},[883],[574,1105],{"className":1106,"style":879},[878],[574,1108,1110,1114],{"className":1109},[608],[574,1111],{"className":1112,"style":1113},[612],"height:0.6444em;",[574,1115,1081],{"className":1116},[617]," gibt es keine Zinsen, dann ist einfach ",[574,1119,1121,1147],{"className":1120},[577],[574,1122,1124],{"className":1123},[581],[583,1125,1126],{"xmlns":585},[587,1127,1128,1144],{},[590,1129,1130,1136,1138,1140,1142],{},[641,1131,1132,1134],{},[593,1133,645],{},[593,1135,648],{},[760,1137,762],{},[593,1139,648],{},[760,1141,767],{},[593,1143,595],{},[597,1145,1146],{"encoding":599},"R_n = n \\cdot r",[574,1148,1150,1205,1223],{"className":1149,"ariaHidden":604},[603],[574,1151,1153,1156,1196,1199,1202],{"className":1152},[608],[574,1154],{"className":1155,"style":661},[612],[574,1157,1159,1162],{"className":1158},[617],[574,1160,645],{"className":1161,"style":668},[617,618],[574,1163,1165],{"className":1164},[672],[574,1166,1168,1188],{"className":1167},[676,677],[574,1169,1171,1185],{"className":1170},[681],[574,1172,1174],{"className":1173,"style":686},[685],[574,1175,1176,1179],{"style":689},[574,1177],{"className":1178,"style":694},[693],[574,1180,1182],{"className":1181},[698,699,700,701],[574,1183,648],{"className":1184},[617,618,701],[574,1186,709],{"className":1187},[708],[574,1189,1191],{"className":1190},[681],[574,1192,1194],{"className":1193,"style":716},[685],[574,1195],{},[574,1197],{"className":1198,"style":879},[878],[574,1200,762],{"className":1201},[883],[574,1203],{"className":1204,"style":879},[878],[574,1206,1208,1211,1214,1217,1220],{"className":1207},[608],[574,1209],{"className":1210,"style":893},[612],[574,1212,648],{"className":1213},[617,618],[574,1215],{"className":1216,"style":900},[878],[574,1218,767],{"className":1219},[904],[574,1221],{"className":1222,"style":900},[878],[574,1224,1226,1229],{"className":1225},[608],[574,1227],{"className":1228,"style":613},[612],[574,1230,595],{"className":1231,"style":619},[617,618],".",[560,1234,1236],{"id":1235},"herleitung","Herleitung",[565,1238,1239,1240,1292,1293,1345],{},"Die Rate aus dem ersten Jahr wird noch ",[574,1241,1243,1261],{"className":1242},[577],[574,1244,1246],{"className":1245},[581],[583,1247,1248],{"xmlns":585},[587,1249,1250,1258],{},[590,1251,1252,1254,1256],{},[593,1253,648],{},[760,1255,787],{},[789,1257,791],{},[597,1259,1260],{"encoding":599},"n - 1",[574,1262,1264,1283],{"className":1263,"ariaHidden":604},[603],[574,1265,1267,1271,1274,1277,1280],{"className":1266},[608],[574,1268],{"className":1269,"style":1270},[612],"height:0.6667em;vertical-align:-0.0833em;",[574,1272,648],{"className":1273},[617,618],[574,1275],{"className":1276,"style":900},[878],[574,1278,787],{"className":1279},[904],[574,1281],{"className":1282,"style":900},[878],[574,1284,1286,1289],{"className":1285},[608],[574,1287],{"className":1288,"style":1113},[612],[574,1290,791],{"className":1291},[617]," Jahre verzinst, die aus dem zweiten Jahr ",[574,1294,1296,1315],{"className":1295},[577],[574,1297,1299],{"className":1298},[581],[583,1300,1301],{"xmlns":585},[587,1302,1303,1312],{},[590,1304,1305,1307,1309],{},[593,1306,648],{},[760,1308,787],{},[789,1310,1311],{},"2",[597,1313,1314],{"encoding":599},"n - 2",[574,1316,1318,1336],{"className":1317,"ariaHidden":604},[603],[574,1319,1321,1324,1327,1330,1333],{"className":1320},[608],[574,1322],{"className":1323,"style":1270},[612],[574,1325,648],{"className":1326},[617,618],[574,1328],{"className":1329,"style":900},[878],[574,1331,787],{"className":1332},[904],[574,1334],{"className":1335,"style":900},[878],[574,1337,1339,1342],{"className":1338},[608],[574,1340],{"className":1341,"style":1113},[612],[574,1343,1311],{"className":1344},[617]," Jahre usw. Das Guthaben ist eine geometrische Summe:",[574,1347,1349],{"className":1348},[734],[574,1350,1352,1452],{"className":1351},[577],[574,1353,1355],{"className":1354},[581],[583,1356,1357],{"xmlns":585,"display":743},[587,1358,1359,1449],{},[590,1360,1361,1367,1369,1371,1373,1385,1388,1390,1392,1404,1406,1409,1411,1413,1415,1417,1419,1421,1423,1425,1427],{},[641,1362,1363,1365],{},[593,1364,645],{},[593,1366,648],{},[760,1368,762],{},[593,1370,595],{},[760,1372,767],{},[779,1374,1375,1377],{},[593,1376,770],{},[590,1378,1379,1381,1383],{},[593,1380,648],{},[760,1382,787],{},[789,1384,791],{},[760,1386,1387],{},"+",[593,1389,595],{},[760,1391,767],{},[779,1393,1394,1396],{},[593,1395,770],{},[590,1397,1398,1400,1402],{},[593,1399,648],{},[760,1401,787],{},[789,1403,1311],{},[760,1405,1387],{},[760,1407,1408],{},"…",[760,1410,1387],{},[593,1412,595],{},[760,1414,767],{},[593,1416,770],{},[760,1418,1387],{},[593,1420,595],{},[760,1422,762],{},[593,1424,595],{},[760,1426,767],{},[774,1428,1429,1441],{},[590,1430,1431,1437,1439],{},[779,1432,1433,1435],{},[593,1434,770],{},[593,1436,648],{},[760,1438,787],{},[789,1440,791],{},[590,1442,1443,1445,1447],{},[593,1444,770],{},[760,1446,787],{},[789,1448,791],{},[597,1450,1451],{"encoding":599},"R_n = r \\cdot q^{n-1} + r \\cdot q^{n-2} + \\ldots + r \\cdot q + r = r \\cdot \\frac{q^n - 1}{q - 1}",[574,1453,1455,1510,1528,1583,1601,1654,1673,1691,1710,1728,1746],{"className":1454,"ariaHidden":604},[603],[574,1456,1458,1461,1501,1504,1507],{"className":1457},[608],[574,1459],{"className":1460,"style":661},[612],[574,1462,1464,1467],{"className":1463},[617],[574,1465,645],{"className":1466,"style":668},[617,618],[574,1468,1470],{"className":1469},[672],[574,1471,1473,1493],{"className":1472},[676,677],[574,1474,1476,1490],{"className":1475},[681],[574,1477,1479],{"className":1478,"style":686},[685],[574,1480,1481,1484],{"style":689},[574,1482],{"className":1483,"style":694},[693],[574,1485,1487],{"className":1486},[698,699,700,701],[574,1488,648],{"className":1489},[617,618,701],[574,1491,709],{"className":1492},[708],[574,1494,1496],{"className":1495},[681],[574,1497,1499],{"className":1498,"style":716},[685],[574,1500],{},[574,1502],{"className":1503,"style":879},[878],[574,1505,762],{"className":1506},[883],[574,1508],{"className":1509,"style":879},[878],[574,1511,1513,1516,1519,1522,1525],{"className":1512},[608],[574,1514],{"className":1515,"style":893},[612],[574,1517,595],{"className":1518,"style":619},[617,618],[574,1520],{"className":1521,"style":900},[878],[574,1523,767],{"className":1524},[904],[574,1526],{"className":1527,"style":900},[878],[574,1529,1531,1535,1574,1577,1580],{"className":1530},[608],[574,1532],{"className":1533,"style":1534},[612],"height:1.0585em;vertical-align:-0.1944em;",[574,1536,1538,1541],{"className":1537},[617],[574,1539,770],{"className":1540,"style":918},[617,618],[574,1542,1544],{"className":1543},[672],[574,1545,1547],{"className":1546},[676],[574,1548,1550],{"className":1549},[681],[574,1551,1554],{"className":1552,"style":1553},[685],"height:0.8641em;",[574,1555,1556,1559],{"style":846},[574,1557],{"className":1558,"style":694},[693],[574,1560,1562],{"className":1561},[698,699,700,701],[574,1563,1565,1568,1571],{"className":1564},[617,701],[574,1566,648],{"className":1567},[617,618,701],[574,1569,787],{"className":1570},[904,701],[574,1572,791],{"className":1573},[617,701],[574,1575],{"className":1576,"style":900},[878],[574,1578,1387],{"className":1579},[904],[574,1581],{"className":1582,"style":900},[878],[574,1584,1586,1589,1592,1595,1598],{"className":1585},[608],[574,1587],{"className":1588,"style":893},[612],[574,1590,595],{"className":1591,"style":619},[617,618],[574,1593],{"className":1594,"style":900},[878],[574,1596,767],{"className":1597},[904],[574,1599],{"className":1600,"style":900},[878],[574,1602,1604,1607,1645,1648,1651],{"className":1603},[608],[574,1605],{"className":1606,"style":1534},[612],[574,1608,1610,1613],{"className":1609},[617],[574,1611,770],{"className":1612,"style":918},[617,618],[574,1614,1616],{"className":1615},[672],[574,1617,1619],{"className":1618},[676],[574,1620,1622],{"className":1621},[681],[574,1623,1625],{"className":1624,"style":1553},[685],[574,1626,1627,1630],{"style":846},[574,1628],{"className":1629,"style":694},[693],[574,1631,1633],{"className":1632},[698,699,700,701],[574,1634,1636,1639,1642],{"className":1635},[617,701],[574,1637,648],{"className":1638},[617,618,701],[574,1640,787],{"className":1641},[904,701],[574,1643,1311],{"className":1644},[617,701],[574,1646],{"className":1647,"style":900},[878],[574,1649,1387],{"className":1650},[904],[574,1652],{"className":1653,"style":900},[878],[574,1655,1657,1660,1664,1667,1670],{"className":1656},[608],[574,1658],{"className":1659,"style":1270},[612],[574,1661,1408],{"className":1662},[1663],"minner",[574,1665],{"className":1666,"style":900},[878],[574,1668,1387],{"className":1669},[904],[574,1671],{"className":1672,"style":900},[878],[574,1674,1676,1679,1682,1685,1688],{"className":1675},[608],[574,1677],{"className":1678,"style":893},[612],[574,1680,595],{"className":1681,"style":619},[617,618],[574,1683],{"className":1684,"style":900},[878],[574,1686,767],{"className":1687},[904],[574,1689],{"className":1690,"style":900},[878],[574,1692,1694,1698,1701,1704,1707],{"className":1693},[608],[574,1695],{"className":1696,"style":1697},[612],"height:0.7778em;vertical-align:-0.1944em;",[574,1699,770],{"className":1700,"style":918},[617,618],[574,1702],{"className":1703,"style":900},[878],[574,1705,1387],{"className":1706},[904],[574,1708],{"className":1709,"style":900},[878],[574,1711,1713,1716,1719,1722,1725],{"className":1712},[608],[574,1714],{"className":1715,"style":613},[612],[574,1717,595],{"className":1718,"style":619},[617,618],[574,1720],{"className":1721,"style":879},[878],[574,1723,762],{"className":1724},[883],[574,1726],{"className":1727,"style":879},[878],[574,1729,1731,1734,1737,1740,1743],{"className":1730},[608],[574,1732],{"className":1733,"style":893},[612],[574,1735,595],{"className":1736,"style":619},[617,618],[574,1738],{"className":1739,"style":900},[878],[574,1741,767],{"className":1742},[904],[574,1744],{"className":1745,"style":900},[878],[574,1747,1749,1752],{"className":1748},[608],[574,1750],{"className":1751,"style":934},[612],[574,1753,1755,1758,1861],{"className":1754},[617],[574,1756],{"className":1757},[941,942],[574,1759,1761],{"className":1760},[774],[574,1762,1764,1853],{"className":1763},[676,677],[574,1765,1767,1850],{"className":1766},[681],[574,1768,1770,1793,1801],{"className":1769,"style":955},[685],[574,1771,1772,1775],{"style":958},[574,1773],{"className":1774,"style":962},[693],[574,1776,1778,1781,1784,1787,1790],{"className":1777},[617],[574,1779,770],{"className":1780,"style":918},[617,618],[574,1782],{"className":1783,"style":900},[878],[574,1785,787],{"className":1786},[904],[574,1788],{"className":1789,"style":900},[878],[574,1791,791],{"className":1792},[617],[574,1794,1795,1798],{"style":983},[574,1796],{"className":1797,"style":962},[693],[574,1799],{"className":1800,"style":991},[990],[574,1802,1803,1806],{"style":994},[574,1804],{"className":1805,"style":962},[693],[574,1807,1809,1838,1841,1844,1847],{"className":1808},[617],[574,1810,1812,1815],{"className":1811},[617],[574,1813,770],{"className":1814,"style":918},[617,618],[574,1816,1818],{"className":1817},[672],[574,1819,1821],{"className":1820},[676],[574,1822,1824],{"className":1823},[681],[574,1825,1827],{"className":1826,"style":1019},[685],[574,1828,1829,1832],{"style":1022},[574,1830],{"className":1831,"style":694},[693],[574,1833,1835],{"className":1834},[698,699,700,701],[574,1836,648],{"className":1837},[617,618,701],[574,1839],{"className":1840,"style":900},[878],[574,1842,787],{"className":1843},[904],[574,1845],{"className":1846,"style":900},[878],[574,1848,791],{"className":1849},[617],[574,1851,709],{"className":1852},[708],[574,1854,1856],{"className":1855},[681],[574,1857,1859],{"className":1858,"style":1053},[685],[574,1860],{},[574,1862],{"className":1863},[1059,942],[560,1865,1867],{"id":1866},"beispiele","Beispiele",[565,1869,1870,1871,1900,1901,1930,1931,1976],{},"Jemand spart ",[574,1872,1874,1888],{"className":1873},[577],[574,1875,1877],{"className":1876},[581],[583,1878,1879],{"xmlns":585},[587,1880,1881,1886],{},[590,1882,1883],{},[789,1884,1885],{},"10",[597,1887,1885],{"encoding":599},[574,1889,1891],{"className":1890,"ariaHidden":604},[603],[574,1892,1894,1897],{"className":1893},[608],[574,1895],{"className":1896,"style":1113},[612],[574,1898,1885],{"className":1899},[617]," Jahre lang jeweils am Jahresende ",[574,1902,1904,1918],{"className":1903},[577],[574,1905,1907],{"className":1906},[581],[583,1908,1909],{"xmlns":585},[587,1910,1911,1916],{},[590,1912,1913],{},[789,1914,1915],{},"1200",[597,1917,1915],{"encoding":599},[574,1919,1921],{"className":1920,"ariaHidden":604},[603],[574,1922,1924,1927],{"className":1923},[608],[574,1925],{"className":1926,"style":1113},[612],[574,1928,1915],{"className":1929},[617]," € bei ",[574,1932,1934,1956],{"className":1933},[577],[574,1935,1937],{"className":1936},[581],[583,1938,1939],{"xmlns":585},[587,1940,1941,1953],{},[590,1942,1943,1946,1949],{},[789,1944,1945],{},"3",[756,1947,1948],{}," ",[593,1950,1952],{"mathvariant":1951},"normal","%",[597,1954,1955],{"encoding":599},"3\\,\\%",[574,1957,1959],{"className":1958,"ariaHidden":604},[603],[574,1960,1962,1966,1969,1973],{"className":1961},[608],[574,1963],{"className":1964,"style":1965},[612],"height:0.8056em;vertical-align:-0.0556em;",[574,1967,1945],{"className":1968},[617],[574,1970],{"className":1971,"style":1972},[878],"margin-right:0.1667em;",[574,1974,1952],{"className":1975},[617]," Zinsen:",[574,1978,1980],{"className":1979},[734],[574,1981,1983,2041],{"className":1982},[577],[574,1984,1986],{"className":1985},[581],[583,1987,1988],{"xmlns":585,"display":743},[587,1989,1990,2038],{},[590,1991,1992,1998,2000,2002,2004,2022,2025,2028,2030,2033,2035],{},[641,1993,1994,1996],{},[593,1995,645],{},[789,1997,1885],{},[760,1999,762],{},[789,2001,1915],{},[760,2003,767],{},[774,2005,2006,2019],{},[590,2007,2008,2015,2017],{},[779,2009,2010,2013],{},[789,2011,2012],{},"1,03",[789,2014,1885],{},[760,2016,787],{},[789,2018,791],{},[789,2020,2021],{},"0,03",[760,2023,2024],{},"≈",[789,2026,2027],{},"13",[756,2029,1948],{},[789,2031,2032],{},"756,66",[756,2034,1948],{},[756,2036,2037],{},"Euro",[597,2039,2040],{"encoding":599},"R_{10} = 1200 \\cdot \\frac{1{,}03^{10} - 1}{0{,}03} \\approx 13\\,756{,}66\\,\\text{Euro}",[574,2042,2044,2103,2121,2266],{"className":2043,"ariaHidden":604},[603],[574,2045,2047,2050,2094,2097,2100],{"className":2046},[608],[574,2048],{"className":2049,"style":661},[612],[574,2051,2053,2056],{"className":2052},[617],[574,2054,645],{"className":2055,"style":668},[617,618],[574,2057,2059],{"className":2058},[672],[574,2060,2062,2086],{"className":2061},[676,677],[574,2063,2065,2083],{"className":2064},[681],[574,2066,2069],{"className":2067,"style":2068},[685],"height:0.3011em;",[574,2070,2071,2074],{"style":689},[574,2072],{"className":2073,"style":694},[693],[574,2075,2077],{"className":2076},[698,699,700,701],[574,2078,2080],{"className":2079},[617,701],[574,2081,1885],{"className":2082},[617,701],[574,2084,709],{"className":2085},[708],[574,2087,2089],{"className":2088},[681],[574,2090,2092],{"className":2091,"style":716},[685],[574,2093],{},[574,2095],{"className":2096,"style":879},[878],[574,2098,762],{"className":2099},[883],[574,2101],{"className":2102,"style":879},[878],[574,2104,2106,2109,2112,2115,2118],{"className":2105},[608],[574,2107],{"className":2108,"style":1113},[612],[574,2110,1915],{"className":2111},[617],[574,2113],{"className":2114,"style":900},[878],[574,2116,767],{"className":2117},[904],[574,2119],{"className":2120,"style":900},[878],[574,2122,2124,2128,2257,2260,2263],{"className":2123},[608],[574,2125],{"className":2126,"style":2127},[612],"height:2.3715em;vertical-align:-0.8804em;",[574,2129,2131,2134,2254],{"className":2130},[617],[574,2132],{"className":2133},[941,942],[574,2135,2137],{"className":2136},[774],[574,2138,2140,2246],{"className":2139},[676,677],[574,2141,2143,2243],{"className":2142},[681],[574,2144,2147,2170,2178],{"className":2145,"style":2146},[685],"height:1.4911em;",[574,2148,2149,2152],{"style":958},[574,2150],{"className":2151,"style":962},[693],[574,2153,2155,2158,2166],{"className":2154},[617],[574,2156,1081],{"className":2157},[617],[574,2159,2161],{"className":2160},[617],[574,2162,2165],{"className":2163},[2164],"mpunct",",",[574,2167,2169],{"className":2168},[617],"03",[574,2171,2172,2175],{"style":983},[574,2173],{"className":2174,"style":962},[693],[574,2176],{"className":2177,"style":991},[990],[574,2179,2180,2183],{"style":994},[574,2181],{"className":2182,"style":962},[693],[574,2184,2186,2189,2195,2198,2231,2234,2237,2240],{"className":2185},[617],[574,2187,791],{"className":2188},[617],[574,2190,2192],{"className":2191},[617],[574,2193,2165],{"className":2194},[2164],[574,2196,1081],{"className":2197},[617],[574,2199,2201,2204],{"className":2200},[617],[574,2202,1945],{"className":2203},[617],[574,2205,2207],{"className":2206},[672],[574,2208,2210],{"className":2209},[676],[574,2211,2213],{"className":2212},[681],[574,2214,2217],{"className":2215,"style":2216},[685],"height:0.8141em;",[574,2218,2219,2222],{"style":1022},[574,2220],{"className":2221,"style":694},[693],[574,2223,2225],{"className":2224},[698,699,700,701],[574,2226,2228],{"className":2227},[617,701],[574,2229,1885],{"className":2230},[617,701],[574,2232],{"className":2233,"style":900},[878],[574,2235,787],{"className":2236},[904],[574,2238],{"className":2239,"style":900},[878],[574,2241,791],{"className":2242},[617],[574,2244,709],{"className":2245},[708],[574,2247,2249],{"className":2248},[681],[574,2250,2252],{"className":2251,"style":1053},[685],[574,2253],{},[574,2255],{"className":2256},[1059,942],[574,2258],{"className":2259,"style":879},[878],[574,2261,2024],{"className":2262},[883],[574,2264],{"className":2265,"style":879},[878],[574,2267,2269,2273,2276,2279,2283,2289,2293,2296],{"className":2268},[608],[574,2270],{"className":2271,"style":2272},[612],"height:0.8778em;vertical-align:-0.1944em;",[574,2274,2027],{"className":2275},[617],[574,2277],{"className":2278,"style":1972},[878],[574,2280,2282],{"className":2281},[617],"756",[574,2284,2286],{"className":2285},[617],[574,2287,2165],{"className":2288},[2164],[574,2290,2292],{"className":2291},[617],"66",[574,2294],{"className":2295,"style":1972},[878],[574,2297,2299],{"className":2298},[617,859],[574,2300,2037],{"className":2301},[617],[565,2303,2304,2305,2390,2391,2432,2433,2705],{},"Eingezahlt wurden ",[574,2306,2308,2336],{"className":2307},[577],[574,2309,2311],{"className":2310},[581],[583,2312,2313],{"xmlns":585},[587,2314,2315,2333],{},[590,2316,2317,2319,2321,2323,2325,2328,2330],{},[789,2318,1885],{},[760,2320,767],{},[789,2322,1915],{},[760,2324,762],{},[789,2326,2327],{},"12",[756,2329,1948],{},[789,2331,2332],{},"000",[597,2334,2335],{"encoding":599},"10 \\cdot 1200 = 12\\,000",[574,2337,2339,2357,2375],{"className":2338,"ariaHidden":604},[603],[574,2340,2342,2345,2348,2351,2354],{"className":2341},[608],[574,2343],{"className":2344,"style":1113},[612],[574,2346,1885],{"className":2347},[617],[574,2349],{"className":2350,"style":900},[878],[574,2352,767],{"className":2353},[904],[574,2355],{"className":2356,"style":900},[878],[574,2358,2360,2363,2366,2369,2372],{"className":2359},[608],[574,2361],{"className":2362,"style":1113},[612],[574,2364,1915],{"className":2365},[617],[574,2367],{"className":2368,"style":879},[878],[574,2370,762],{"className":2371},[883],[574,2373],{"className":2374,"style":879},[878],[574,2376,2378,2381,2384,2387],{"className":2377},[608],[574,2379],{"className":2380,"style":1113},[612],[574,2382,2327],{"className":2383},[617],[574,2385],{"className":2386,"style":1972},[878],[574,2388,2332],{"className":2389},[617]," €, die Zinsen machen also ",[574,2392,2394,2409],{"className":2393},[577],[574,2395,2397],{"className":2396},[581],[583,2398,2399],{"xmlns":585},[587,2400,2401,2406],{},[590,2402,2403],{},[789,2404,2405],{},"1756,66",[597,2407,2408],{"encoding":599},"1756{,}66",[574,2410,2412],{"className":2411,"ariaHidden":604},[603],[574,2413,2415,2419,2423,2429],{"className":2414},[608],[574,2416],{"className":2417,"style":2418},[612],"height:0.8389em;vertical-align:-0.1944em;",[574,2420,2422],{"className":2421},[617],"1756",[574,2424,2426],{"className":2425},[617],[574,2427,2165],{"className":2428},[2164],[574,2430,2292],{"className":2431},[617]," € aus. Werden die Raten am Jahresanfang gezahlt, ergeben sich ",[574,2434,2436,2482],{"className":2435},[577],[574,2437,2439],{"className":2438},[581],[583,2440,2441],{"xmlns":585},[587,2442,2443,2479],{},[590,2444,2445,2447,2449,2451,2453,2469,2471,2474,2476],{},[789,2446,1915],{},[760,2448,767],{},[789,2450,2012],{},[760,2452,767],{},[774,2454,2455,2467],{},[590,2456,2457,2463,2465],{},[779,2458,2459,2461],{},[789,2460,2012],{},[789,2462,1885],{},[760,2464,787],{},[789,2466,791],{},[789,2468,2021],{},[760,2470,2024],{},[789,2472,2473],{},"14",[756,2475,1948],{},[789,2477,2478],{},"169,35",[597,2480,2481],{"encoding":599},"1200 \\cdot 1{,}03 \\cdot \\frac{1{,}03^{10} - 1}{0{,}03} \\approx 14\\,169{,}35",[574,2483,2485,2503,2530,2679],{"className":2484,"ariaHidden":604},[603],[574,2486,2488,2491,2494,2497,2500],{"className":2487},[608],[574,2489],{"className":2490,"style":1113},[612],[574,2492,1915],{"className":2493},[617],[574,2495],{"className":2496,"style":900},[878],[574,2498,767],{"className":2499},[904],[574,2501],{"className":2502,"style":900},[878],[574,2504,2506,2509,2512,2518,2521,2524,2527],{"className":2505},[608],[574,2507],{"className":2508,"style":2418},[612],[574,2510,791],{"className":2511},[617],[574,2513,2515],{"className":2514},[617],[574,2516,2165],{"className":2517},[2164],[574,2519,2169],{"className":2520},[617],[574,2522],{"className":2523,"style":900},[878],[574,2525,767],{"className":2526},[904],[574,2528],{"className":2529,"style":900},[878],[574,2531,2533,2537,2670,2673,2676],{"className":2532},[608],[574,2534],{"className":2535,"style":2536},[612],"height:1.5511em;vertical-align:-0.4811em;",[574,2538,2540,2543,2667],{"className":2539},[617],[574,2541],{"className":2542},[941,942],[574,2544,2546],{"className":2545},[774],[574,2547,2549,2658],{"className":2548},[676,677],[574,2550,2552,2655],{"className":2551},[681],[574,2553,2556,2580,2588],{"className":2554,"style":2555},[685],"height:1.07em;",[574,2557,2559,2562],{"style":2558},"top:-2.655em;",[574,2560],{"className":2561,"style":962},[693],[574,2563,2565],{"className":2564},[698,699,700,701],[574,2566,2568,2571,2577],{"className":2567},[617,701],[574,2569,1081],{"className":2570},[617,701],[574,2572,2574],{"className":2573},[617,701],[574,2575,2165],{"className":2576},[2164,701],[574,2578,2169],{"className":2579},[617,701],[574,2581,2582,2585],{"style":983},[574,2583],{"className":2584,"style":962},[693],[574,2586],{"className":2587,"style":991},[990],[574,2589,2591,2594],{"style":2590},"top:-3.4461em;",[574,2592],{"className":2593,"style":962},[693],[574,2595,2597],{"className":2596},[698,699,700,701],[574,2598,2600,2603,2609,2612,2649,2652],{"className":2599},[617,701],[574,2601,791],{"className":2602},[617,701],[574,2604,2606],{"className":2605},[617,701],[574,2607,2165],{"className":2608},[2164,701],[574,2610,1081],{"className":2611},[617,701],[574,2613,2615,2618],{"className":2614},[617,701],[574,2616,1945],{"className":2617},[617,701],[574,2619,2621],{"className":2620},[672],[574,2622,2624],{"className":2623},[676],[574,2625,2627],{"className":2626},[681],[574,2628,2631],{"className":2629,"style":2630},[685],"height:0.8913em;",[574,2632,2634,2638],{"style":2633},"top:-2.931em;margin-right:0.0714em;",[574,2635],{"className":2636,"style":2637},[693],"height:2.5em;",[574,2639,2643],{"className":2640},[698,2641,2642,701],"reset-size3","size1",[574,2644,2646],{"className":2645},[617,701],[574,2647,1885],{"className":2648},[617,701],[574,2650,787],{"className":2651},[904,701],[574,2653,791],{"className":2654},[617,701],[574,2656,709],{"className":2657},[708],[574,2659,2661],{"className":2660},[681],[574,2662,2665],{"className":2663,"style":2664},[685],"height:0.4811em;",[574,2666],{},[574,2668],{"className":2669},[1059,942],[574,2671],{"className":2672,"style":879},[878],[574,2674,2024],{"className":2675},[883],[574,2677],{"className":2678,"style":879},[878],[574,2680,2682,2685,2688,2691,2695,2701],{"className":2681},[608],[574,2683],{"className":2684,"style":2418},[612],[574,2686,2473],{"className":2687},[617],[574,2689],{"className":2690,"style":1972},[878],[574,2692,2694],{"className":2693},[617],"169",[574,2696,2698],{"className":2697},[617],[574,2699,2165],{"className":2700},[2164],[574,2702,2704],{"className":2703},[617],"35"," €.",[565,2707,2708,2709,2738,2739,2790,2791,2831,2832,2860],{},"Welche Jahresrate braucht man, um in ",[574,2710,2712,2726],{"className":2711},[577],[574,2713,2715],{"className":2714},[581],[583,2716,2717],{"xmlns":585},[587,2718,2719,2724],{},[590,2720,2721],{},[789,2722,2723],{},"8",[597,2725,2723],{"encoding":599},[574,2727,2729],{"className":2728,"ariaHidden":604},[603],[574,2730,2732,2735],{"className":2731},[608],[574,2733],{"className":2734,"style":1113},[612],[574,2736,2723],{"className":2737},[617]," Jahren bei ",[574,2740,2742,2761],{"className":2741},[577],[574,2743,2745],{"className":2744},[581],[583,2746,2747],{"xmlns":585},[587,2748,2749,2758],{},[590,2750,2751,2754,2756],{},[789,2752,2753],{},"2,5",[756,2755,1948],{},[593,2757,1952],{"mathvariant":1951},[597,2759,2760],{"encoding":599},"2{,}5\\,\\%",[574,2762,2764],{"className":2763,"ariaHidden":604},[603],[574,2765,2767,2771,2774,2780,2784,2787],{"className":2766},[608],[574,2768],{"className":2769,"style":2770},[612],"height:0.9444em;vertical-align:-0.1944em;",[574,2772,1311],{"className":2773},[617],[574,2775,2777],{"className":2776},[617],[574,2778,2165],{"className":2779},[2164],[574,2781,2783],{"className":2782},[617],"5",[574,2785],{"className":2786,"style":1972},[878],[574,2788,1952],{"className":2789},[617]," auf ",[574,2792,2794,2813],{"className":2793},[577],[574,2795,2797],{"className":2796},[581],[583,2798,2799],{"xmlns":585},[587,2800,2801,2810],{},[590,2802,2803,2806,2808],{},[789,2804,2805],{},"20",[756,2807,1948],{},[789,2809,2332],{},[597,2811,2812],{"encoding":599},"20\\,000",[574,2814,2816],{"className":2815,"ariaHidden":604},[603],[574,2817,2819,2822,2825,2828],{"className":2818},[608],[574,2820],{"className":2821,"style":1113},[612],[574,2823,2805],{"className":2824},[617],[574,2826],{"className":2827,"style":1972},[878],[574,2829,2332],{"className":2830},[617]," € zu kommen? Umgestellt nach ",[574,2833,2835,2848],{"className":2834},[577],[574,2836,2838],{"className":2837},[581],[583,2839,2840],{"xmlns":585},[587,2841,2842,2846],{},[590,2843,2844],{},[593,2845,595],{},[597,2847,595],{"encoding":599},[574,2849,2851],{"className":2850,"ariaHidden":604},[603],[574,2852,2854,2857],{"className":2853},[608],[574,2855],{"className":2856,"style":613},[612],[574,2858,595],{"className":2859,"style":619},[617,618],":",[574,2862,2864],{"className":2863},[734],[574,2865,2867,2950],{"className":2866},[577],[574,2868,2870],{"className":2869},[581],[583,2871,2872],{"xmlns":585,"display":743},[587,2873,2874,2947],{},[590,2875,2876,2878,2880,2886,2888,2910,2912,2914,2916,2918,2920,2938,2940,2943,2945],{},[593,2877,595],{},[760,2879,762],{},[641,2881,2882,2884],{},[593,2883,645],{},[593,2885,648],{},[760,2887,767],{},[774,2889,2890,2898],{},[590,2891,2892,2894,2896],{},[593,2893,770],{},[760,2895,787],{},[789,2897,791],{},[590,2899,2900,2906,2908],{},[779,2901,2902,2904],{},[593,2903,770],{},[593,2905,648],{},[760,2907,787],{},[789,2909,791],{},[760,2911,762],{},[789,2913,2805],{},[756,2915,1948],{},[789,2917,2332],{},[760,2919,767],{},[774,2921,2922,2925],{},[789,2923,2924],{},"0,025",[590,2926,2927,2934,2936],{},[779,2928,2929,2932],{},[789,2930,2931],{},"1,025",[789,2933,2723],{},[760,2935,787],{},[789,2937,791],{},[760,2939,2024],{},[789,2941,2942],{},"2289,35",[756,2944,1948],{},[756,2946,2037],{},[597,2948,2949],{"encoding":599},"r = R_n \\cdot \\frac{q - 1}{q^n - 1} = 20\\,000 \\cdot \\frac{0{,}025}{1{,}025^8 - 1} \\approx 2289{,}35\\,\\text{Euro}",[574,2951,2953,2971,3026,3157,3181,3320],{"className":2952,"ariaHidden":604},[603],[574,2954,2956,2959,2962,2965,2968],{"className":2955},[608],[574,2957],{"className":2958,"style":613},[612],[574,2960,595],{"className":2961,"style":619},[617,618],[574,2963],{"className":2964,"style":879},[878],[574,2966,762],{"className":2967},[883],[574,2969],{"className":2970,"style":879},[878],[574,2972,2974,2977,3017,3020,3023],{"className":2973},[608],[574,2975],{"className":2976,"style":661},[612],[574,2978,2980,2983],{"className":2979},[617],[574,2981,645],{"className":2982,"style":668},[617,618],[574,2984,2986],{"className":2985},[672],[574,2987,2989,3009],{"className":2988},[676,677],[574,2990,2992,3006],{"className":2991},[681],[574,2993,2995],{"className":2994,"style":686},[685],[574,2996,2997,3000],{"style":689},[574,2998],{"className":2999,"style":694},[693],[574,3001,3003],{"className":3002},[698,699,700,701],[574,3004,648],{"className":3005},[617,618,701],[574,3007,709],{"className":3008},[708],[574,3010,3012],{"className":3011},[681],[574,3013,3015],{"className":3014,"style":716},[685],[574,3016],{},[574,3018],{"className":3019,"style":900},[878],[574,3021,767],{"className":3022},[904],[574,3024],{"className":3025,"style":900},[878],[574,3027,3029,3033,3148,3151,3154],{"className":3028},[608],[574,3030],{"className":3031,"style":3032},[612],"height:2.2019em;vertical-align:-0.8804em;",[574,3034,3036,3039,3145],{"className":3035},[617],[574,3037],{"className":3038},[941,942],[574,3040,3042],{"className":3041},[774],[574,3043,3045,3137],{"className":3044},[676,677],[574,3046,3048,3134],{"className":3047},[681],[574,3049,3052,3103,3111],{"className":3050,"style":3051},[685],"height:1.3214em;",[574,3053,3054,3057],{"style":958},[574,3055],{"className":3056,"style":962},[693],[574,3058,3060,3091,3094,3097,3100],{"className":3059},[617],[574,3061,3063,3066],{"className":3062},[617],[574,3064,770],{"className":3065,"style":918},[617,618],[574,3067,3069],{"className":3068},[672],[574,3070,3072],{"className":3071},[676],[574,3073,3075],{"className":3074},[681],[574,3076,3079],{"className":3077,"style":3078},[685],"height:0.5904em;",[574,3080,3082,3085],{"style":3081},"top:-2.989em;margin-right:0.05em;",[574,3083],{"className":3084,"style":694},[693],[574,3086,3088],{"className":3087},[698,699,700,701],[574,3089,648],{"className":3090},[617,618,701],[574,3092],{"className":3093,"style":900},[878],[574,3095,787],{"className":3096},[904],[574,3098],{"className":3099,"style":900},[878],[574,3101,791],{"className":3102},[617],[574,3104,3105,3108],{"style":983},[574,3106],{"className":3107,"style":962},[693],[574,3109],{"className":3110,"style":991},[990],[574,3112,3113,3116],{"style":994},[574,3114],{"className":3115,"style":962},[693],[574,3117,3119,3122,3125,3128,3131],{"className":3118},[617],[574,3120,770],{"className":3121,"style":918},[617,618],[574,3123],{"className":3124,"style":900},[878],[574,3126,787],{"className":3127},[904],[574,3129],{"className":3130,"style":900},[878],[574,3132,791],{"className":3133},[617],[574,3135,709],{"className":3136},[708],[574,3138,3140],{"className":3139},[681],[574,3141,3143],{"className":3142,"style":1053},[685],[574,3144],{},[574,3146],{"className":3147},[1059,942],[574,3149],{"className":3150,"style":879},[878],[574,3152,762],{"className":3153},[883],[574,3155],{"className":3156,"style":879},[878],[574,3158,3160,3163,3166,3169,3172,3175,3178],{"className":3159},[608],[574,3161],{"className":3162,"style":1113},[612],[574,3164,2805],{"className":3165},[617],[574,3167],{"className":3168,"style":1972},[878],[574,3170,2332],{"className":3171},[617],[574,3173],{"className":3174,"style":900},[878],[574,3176,767],{"className":3177},[904],[574,3179],{"className":3180,"style":900},[878],[574,3182,3184,3187,3311,3314,3317],{"className":3183},[608],[574,3185],{"className":3186,"style":3032},[612],[574,3188,3190,3193,3308],{"className":3189},[617],[574,3191],{"className":3192},[941,942],[574,3194,3196],{"className":3195},[774],[574,3197,3199,3300],{"className":3198},[676,677],[574,3200,3202,3297],{"className":3201},[681],[574,3203,3205,3268,3276],{"className":3204,"style":3051},[685],[574,3206,3207,3210],{"style":958},[574,3208],{"className":3209,"style":962},[693],[574,3211,3213,3216,3222,3226,3256,3259,3262,3265],{"className":3212},[617],[574,3214,791],{"className":3215},[617],[574,3217,3219],{"className":3218},[617],[574,3220,2165],{"className":3221},[2164],[574,3223,3225],{"className":3224},[617],"02",[574,3227,3229,3232],{"className":3228},[617],[574,3230,2783],{"className":3231},[617],[574,3233,3235],{"className":3234},[672],[574,3236,3238],{"className":3237},[676],[574,3239,3241],{"className":3240},[681],[574,3242,3245],{"className":3243,"style":3244},[685],"height:0.7401em;",[574,3246,3247,3250],{"style":3081},[574,3248],{"className":3249,"style":694},[693],[574,3251,3253],{"className":3252},[698,699,700,701],[574,3254,2723],{"className":3255},[617,701],[574,3257],{"className":3258,"style":900},[878],[574,3260,787],{"className":3261},[904],[574,3263],{"className":3264,"style":900},[878],[574,3266,791],{"className":3267},[617],[574,3269,3270,3273],{"style":983},[574,3271],{"className":3272,"style":962},[693],[574,3274],{"className":3275,"style":991},[990],[574,3277,3278,3281],{"style":994},[574,3279],{"className":3280,"style":962},[693],[574,3282,3284,3287,3293],{"className":3283},[617],[574,3285,1081],{"className":3286},[617],[574,3288,3290],{"className":3289},[617],[574,3291,2165],{"className":3292},[2164],[574,3294,3296],{"className":3295},[617],"025",[574,3298,709],{"className":3299},[708],[574,3301,3303],{"className":3302},[681],[574,3304,3306],{"className":3305,"style":1053},[685],[574,3307],{},[574,3309],{"className":3310},[1059,942],[574,3312],{"className":3313,"style":879},[878],[574,3315,2024],{"className":3316},[883],[574,3318],{"className":3319,"style":879},[878],[574,3321,3323,3326,3330,3336,3339,3342],{"className":3322},[608],[574,3324],{"className":3325,"style":2272},[612],[574,3327,3329],{"className":3328},[617],"2289",[574,3331,3333],{"className":3332},[617],[574,3334,2165],{"className":3335},[2164],[574,3337,2704],{"className":3338},[617],[574,3340],{"className":3341,"style":1972},[878],[574,3343,3345],{"className":3344},[617,859],[574,3346,2037],{"className":3347},[617],[560,3349,3351],{"id":3350},"typische-fehler","Typische Fehler",[3353,3354,3355,3612,3643,3751],"ul",{},[3356,3357,3358,3359,3387,3388,3534,3535,3573,3574,1232],"li",{},"Mit ",[574,3360,3362,3375],{"className":3361},[577],[574,3363,3365],{"className":3364},[581],[583,3366,3367],{"xmlns":585},[587,3368,3369,3373],{},[590,3370,3371],{},[593,3372,565],{},[597,3374,565],{"encoding":599},[574,3376,3378],{"className":3377,"ariaHidden":604},[603],[574,3379,3381,3384],{"className":3380},[608],[574,3382],{"className":3383,"style":1094},[612],[574,3385,565],{"className":3386},[617,618]," statt mit ",[574,3389,3391,3418],{"className":3390},[577],[574,3392,3394],{"className":3393},[581],[583,3395,3396],{"xmlns":585},[587,3397,3398,3415],{},[590,3399,3400,3402,3404,3406,3408],{},[593,3401,770],{},[760,3403,787],{},[789,3405,791],{},[760,3407,762],{},[774,3409,3410,3412],{},[593,3411,565],{},[789,3413,3414],{},"100",[597,3416,3417],{"encoding":599},"q - 1 = \\frac{p}{100}",[574,3419,3421,3439,3457],{"className":3420,"ariaHidden":604},[603],[574,3422,3424,3427,3430,3433,3436],{"className":3423},[608],[574,3425],{"className":3426,"style":1697},[612],[574,3428,770],{"className":3429,"style":918},[617,618],[574,3431],{"className":3432,"style":900},[878],[574,3434,787],{"className":3435},[904],[574,3437],{"className":3438,"style":900},[878],[574,3440,3442,3445,3448,3451,3454],{"className":3441},[608],[574,3443],{"className":3444,"style":1113},[612],[574,3446,791],{"className":3447},[617],[574,3449],{"className":3450,"style":879},[878],[574,3452,762],{"className":3453},[883],[574,3455],{"className":3456,"style":879},[878],[574,3458,3460,3464],{"className":3459},[608],[574,3461],{"className":3462,"style":3463},[612],"height:1.0925em;vertical-align:-0.345em;",[574,3465,3467,3470,3531],{"className":3466},[617],[574,3468],{"className":3469},[941,942],[574,3471,3473],{"className":3472},[774],[574,3474,3476,3522],{"className":3475},[676,677],[574,3477,3479,3519],{"className":3478},[681],[574,3480,3483,3497,3505],{"className":3481,"style":3482},[685],"height:0.7475em;",[574,3484,3485,3488],{"style":2558},[574,3486],{"className":3487,"style":962},[693],[574,3489,3491],{"className":3490},[698,699,700,701],[574,3492,3494],{"className":3493},[617,701],[574,3495,3414],{"className":3496},[617,701],[574,3498,3499,3502],{"style":983},[574,3500],{"className":3501,"style":962},[693],[574,3503],{"className":3504,"style":991},[990],[574,3506,3507,3510],{"style":2590},[574,3508],{"className":3509,"style":962},[693],[574,3511,3513],{"className":3512},[698,699,700,701],[574,3514,3516],{"className":3515},[617,701],[574,3517,565],{"className":3518},[617,618,701],[574,3520,709],{"className":3521},[708],[574,3523,3525],{"className":3524},[681],[574,3526,3529],{"className":3527,"style":3528},[685],"height:0.345em;",[574,3530],{},[574,3532],{"className":3533},[1059,942]," im Nenner rechnen. Bei ",[574,3536,3538,3555],{"className":3537},[577],[574,3539,3541],{"className":3540},[581],[583,3542,3543],{"xmlns":585},[587,3544,3545,3553],{},[590,3546,3547,3549,3551],{},[789,3548,1945],{},[756,3550,1948],{},[593,3552,1952],{"mathvariant":1951},[597,3554,1955],{"encoding":599},[574,3556,3558],{"className":3557,"ariaHidden":604},[603],[574,3559,3561,3564,3567,3570],{"className":3560},[608],[574,3562],{"className":3563,"style":1965},[612],[574,3565,1945],{"className":3566},[617],[574,3568],{"className":3569,"style":1972},[878],[574,3571,1952],{"className":3572},[617]," ist der Nenner ",[574,3575,3577,3591],{"className":3576},[577],[574,3578,3580],{"className":3579},[581],[583,3581,3582],{"xmlns":585},[587,3583,3584,3588],{},[590,3585,3586],{},[789,3587,2021],{},[597,3589,3590],{"encoding":599},"0{,}03",[574,3592,3594],{"className":3593,"ariaHidden":604},[603],[574,3595,3597,3600,3603,3609],{"className":3596},[608],[574,3598],{"className":3599,"style":2418},[612],[574,3601,1081],{"className":3602},[617],[574,3604,3606],{"className":3605},[617],[574,3607,2165],{"className":3608},[2164],[574,3610,2169],{"className":3611},[617],[3356,3613,3614,3615,1232],{},"Nachschüssig und vorschüssig verwechseln. Am Jahresanfang eingezahlte Raten bringen den zusätzlichen Faktor ",[574,3616,3618,3631],{"className":3617},[577],[574,3619,3621],{"className":3620},[581],[583,3622,3623],{"xmlns":585},[587,3624,3625,3629],{},[590,3626,3627],{},[593,3628,770],{},[597,3630,770],{"encoding":599},[574,3632,3634],{"className":3633,"ariaHidden":604},[603],[574,3635,3637,3640],{"className":3636},[608],[574,3638],{"className":3639,"style":1094},[612],[574,3641,770],{"className":3642,"style":918},[617,618],[3356,3644,3645,3646,3750],{},"Jede Rate gleich lang verzinsen, also ",[574,3647,3649,3675],{"className":3648},[577],[574,3650,3652],{"className":3651},[581],[583,3653,3654],{"xmlns":585},[587,3655,3656,3672],{},[590,3657,3658,3660,3662,3664,3666],{},[593,3659,648],{},[760,3661,767],{},[593,3663,595],{},[760,3665,767],{},[779,3667,3668,3670],{},[593,3669,770],{},[593,3671,648],{},[597,3673,3674],{"encoding":599},"n \\cdot r \\cdot q^n",[574,3676,3678,3696,3714],{"className":3677,"ariaHidden":604},[603],[574,3679,3681,3684,3687,3690,3693],{"className":3680},[608],[574,3682],{"className":3683,"style":893},[612],[574,3685,648],{"className":3686},[617,618],[574,3688],{"className":3689,"style":900},[878],[574,3691,767],{"className":3692},[904],[574,3694],{"className":3695,"style":900},[878],[574,3697,3699,3702,3705,3708,3711],{"className":3698},[608],[574,3700],{"className":3701,"style":893},[612],[574,3703,595],{"className":3704,"style":619},[617,618],[574,3706],{"className":3707,"style":900},[878],[574,3709,767],{"className":3710},[904],[574,3712],{"className":3713,"style":900},[878],[574,3715,3717,3721],{"className":3716},[608],[574,3718],{"className":3719,"style":3720},[612],"height:0.8588em;vertical-align:-0.1944em;",[574,3722,3724,3727],{"className":3723},[617],[574,3725,770],{"className":3726,"style":918},[617,618],[574,3728,3730],{"className":3729},[672],[574,3731,3733],{"className":3732},[676],[574,3734,3736],{"className":3735},[681],[574,3737,3739],{"className":3738,"style":1019},[685],[574,3740,3741,3744],{"style":1022},[574,3742],{"className":3743,"style":694},[693],[574,3745,3747],{"className":3746},[698,699,700,701],[574,3748,648],{"className":3749},[617,618,701]," rechnen.",[3356,3752,3753],{},"Monatliche Raten mit einem Jahreszins in die Formel einsetzen, ohne Zins oder Raten umzurechnen.",{"title":3755,"searchDepth":3756,"depth":3756,"links":3757},"",2,[3758,3759,3760,3761],{"id":562,"depth":3756,"text":563},{"id":1235,"depth":3756,"text":1236},{"id":1866,"depth":3756,"text":1867},{"id":3350,"depth":3756,"text":3351},[3763,3766,3769,3772,3775,3778],{"lhs":3764,"rhs":3765},"r*q^3 + r*q^2 + r*q + r","r*(q^4 - 1)\u002F(q - 1)",{"lhs":3767,"rhs":3768},"round(1200 * (1.03^10 - 1) \u002F 0.03, 2)","13756.66",{"lhs":3770,"rhs":3771},"10 * 1200","12000",{"lhs":3773,"rhs":3774},"round(1200 * (1.03^10 - 1) \u002F 0.03 - 12000, 2)","1756.66",{"lhs":3776,"rhs":3777},"round(1200 * 1.03 * (1.03^10 - 1) \u002F 0.03, 2)","14169.35",{"lhs":3779,"rhs":3780},"round(20000 * 0.025 \u002F (1.025^8 - 1), 2)","2289.35","p > 0,\\ n \\geq 1,\\ \\text{Einzahlung jeweils am Ende des Jahres}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p > 0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7335em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\geq 1,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">Einzahlung jeweils am Ende des Jahres\u003C\u002Fspan>",null,"md","annuity-future-value","R_n = r \\cdot \\frac{q^n - 1}{q - 1}, \\qquad q = 1 + \\frac{p}{100}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>R\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>r\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmsup>\u003Cmi>q\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>q\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmi>q\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>+\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>100\u003C\u002Fmn>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">R_n = r \\cdot \\frac{q^n - 1}{q - 1}, \\qquad q = 1 + \\frac{p}{100}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4445em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.2218em;vertical-align:-0.8804em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3414em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6644em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8804em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:2em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7278em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.7936em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1076em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">100\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Farithmetic\u002Frentenendwert",[],[3794,3795,3796,3797],"compound-interest","geometric-sum","annuity-present-value","annuity-payment",{"title":548,"description":3755},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Frentenendwert","Zahlt man n Jahre lang jeweils am Jahresende r ein, wächst das Guthaben mit Zinseszins auf r · (qⁿ − 1)\u002F(q − 1).",[3802,3803,3804,3805,3806],"sparplan","rente","zinseszins","geometrische reihe","finanzmathematik",[3808,3811,3814,3817,3820],{"symbol":651,"meaning":3809,"symbolHtml":3810},"Rentenendwert, das angesparte Kapital nach n Jahren","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>R\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">R_n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":595,"meaning":3812,"symbolHtml":3813},"Rate, der Betrag, der jedes Jahr eingezahlt wird","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">r\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":770,"meaning":3815,"symbolHtml":3816},"Zinsfaktor","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>q\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">q\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":565,"meaning":3818,"symbolHtml":3819},"Zinssatz in Prozent pro Jahr","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":648,"meaning":3821,"symbolHtml":3822},"Anzahl der Jahre und damit der Raten","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","yE4E1AV1AUjKCnIg3vHAjXczUFwHoWLuKICL3qA0R6A",[3825,3828,3831,3834],{"stem":3826,"title":3827,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fannuitaet","Annuität",{"stem":3829,"title":3830,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Frentenbarwert","Rentenbarwert",{"stem":3832,"title":3833,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fzinseszins","Zinseszins",{"stem":3835,"title":3836,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fendliche-geometrische-reihe","Endliche geometrische Reihe",1793824260071]