[{"data":1,"prerenderedAt":3323},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Farithmetic\u002Faenderungsfaktor":546,"formula-related-de\u002Fformulas\u002Fmath\u002Farithmetic\u002Faenderungsfaktor":3310},[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":3251,"conditions":3272,"conditionsHtml":3273,"deprecated":3274,"description":3245,"extension":3275,"figure":3274,"figureCaption":3274,"figureHtml":3274,"formulaId":3276,"latex":3277,"latexHtml":3278,"level":3279,"meta":3280,"navigation":3281,"path":3282,"redirectFrom":3283,"related":3284,"seo":3289,"stem":3290,"subject":578,"summary":3291,"tags":3292,"variables":3298,"__hash__":3309},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Farithmetic\u002Faenderungsfaktor.md","Vermehrter und verminderter Grundwert",[550,551,552,553,554,555],"Änderungsfaktor","Wachstumsfaktor","vermehrter Grundwert","verminderter Grundwert","Preis nach Rabatt","Preis vor Erhöhung berechnen",{"type":557,"value":558,"toc":3244},"minimark",[559,564,916,1238,1466,1680,1777,1781,1854,2017,2090,2398,2472,2624,2656,2660],[560,561,563],"h2",{"id":562},"erklärung","Erklärung",[565,566,567,568,630,631,673,674,712,713,794,795,799,800,838,839,911,912,915],"p",{},"Steigt ein Wert um ",[569,570,573,603],"span",{"className":571},[572],"katex",[569,574,577],{"className":575},[576],"katex-mathml",[578,579,581],"math",{"xmlns":580},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[582,583,584,598],"semantics",{},[585,586,587,590,594],"mrow",{},[588,589,565],"mi",{},[591,592,593],"mtext",{}," ",[588,595,597],{"mathvariant":596},"normal","%",[599,600,602],"annotation",{"encoding":601},"application\u002Fx-tex","p\\,\\%",[569,604,608],{"className":605,"ariaHidden":607},[606],"katex-html","true",[569,609,612,617,622,627],{"className":610},[611],"base",[569,613],{"className":614,"style":616},[615],"strut","height:0.9444em;vertical-align:-0.1944em;",[569,618,565],{"className":619},[620,621],"mord","mathnormal",[569,623],{"className":624,"style":626},[625],"mspace","margin-right:0.1667em;",[569,628,597],{"className":629},[620],", kommt zum Grundwert (",[569,632,634,654],{"className":633},[572],[569,635,637],{"className":636},[576],[578,638,639],{"xmlns":580},[582,640,641,651],{},[585,642,643,647,649],{},[644,645,646],"mn",{},"100",[591,648,593],{},[588,650,597],{"mathvariant":596},[599,652,653],{"encoding":601},"100\\,\\%",[569,655,657],{"className":656,"ariaHidden":607},[606],[569,658,660,664,667,670],{"className":659},[611],[569,661],{"className":662,"style":663},[615],"height:0.8056em;vertical-align:-0.0556em;",[569,665,646],{"className":666},[620],[569,668],{"className":669,"style":626},[625],[569,671,597],{"className":672},[620],") noch der Anteil ",[569,675,677,694],{"className":676},[572],[569,678,680],{"className":679},[576],[578,681,682],{"xmlns":580},[582,683,684,692],{},[585,685,686,688,690],{},[588,687,565],{},[591,689,593],{},[588,691,597],{"mathvariant":596},[599,693,602],{"encoding":601},[569,695,697],{"className":696,"ariaHidden":607},[606],[569,698,700,703,706,709],{"className":699},[611],[569,701],{"className":702,"style":616},[615],[569,704,565],{"className":705},[620,621],[569,707],{"className":708,"style":626},[625],[569,710,597],{"className":711},[620]," dazu. Der neue Wert ist dann ",[569,714,716,747],{"className":715},[572],[569,717,719],{"className":718},[576],[578,720,721],{"xmlns":580},[582,722,723,744],{},[585,724,725,730,732,735,737,740,742],{},[726,727,729],"mo",{"stretchy":728},"false","(",[644,731,646],{},[726,733,734],{},"+",[588,736,565],{},[726,738,739],{"stretchy":728},")",[591,741,593],{},[588,743,597],{"mathvariant":596},[599,745,746],{"encoding":601},"(100 + p)\\,\\%",[569,748,750,775],{"className":749,"ariaHidden":607},[606],[569,751,753,757,761,764,768,772],{"className":752},[611],[569,754],{"className":755,"style":756},[615],"height:1em;vertical-align:-0.25em;",[569,758,729],{"className":759},[760],"mopen",[569,762,646],{"className":763},[620],[569,765],{"className":766,"style":767},[625],"margin-right:0.2222em;",[569,769,734],{"className":770},[771],"mbin",[569,773],{"className":774,"style":767},[625],[569,776,778,781,784,788,791],{"className":777},[611],[569,779],{"className":780,"style":756},[615],[569,782,565],{"className":783},[620,621],[569,785,739],{"className":786},[787],"mclose",[569,789],{"className":790,"style":626},[625],[569,792,597],{"className":793},[620]," des alten. Das ist der ",[796,797,798],"strong",{},"vermehrte Grundwert",". Sinkt der Wert um ",[569,801,803,820],{"className":802},[572],[569,804,806],{"className":805},[576],[578,807,808],{"xmlns":580},[582,809,810,818],{},[585,811,812,814,816],{},[588,813,565],{},[591,815,593],{},[588,817,597],{"mathvariant":596},[599,819,602],{"encoding":601},[569,821,823],{"className":822,"ariaHidden":607},[606],[569,824,826,829,832,835],{"className":825},[611],[569,827],{"className":828,"style":616},[615],[569,830,565],{"className":831},[620,621],[569,833],{"className":834,"style":626},[625],[569,836,597],{"className":837},[620],", bleiben ",[569,840,842,869],{"className":841},[572],[569,843,845],{"className":844},[576],[578,846,847],{"xmlns":580},[582,848,849,866],{},[585,850,851,853,855,858,860,862,864],{},[726,852,729],{"stretchy":728},[644,854,646],{},[726,856,857],{},"−",[588,859,565],{},[726,861,739],{"stretchy":728},[591,863,593],{},[588,865,597],{"mathvariant":596},[599,867,868],{"encoding":601},"(100 - p)\\,\\%",[569,870,872,893],{"className":871,"ariaHidden":607},[606],[569,873,875,878,881,884,887,890],{"className":874},[611],[569,876],{"className":877,"style":756},[615],[569,879,729],{"className":880},[760],[569,882,646],{"className":883},[620],[569,885],{"className":886,"style":767},[625],[569,888,857],{"className":889},[771],[569,891],{"className":892,"style":767},[625],[569,894,896,899,902,905,908],{"className":895},[611],[569,897],{"className":898,"style":756},[615],[569,900,565],{"className":901},[620,621],[569,903,739],{"className":904},[787],[569,906],{"className":907,"style":626},[625],[569,909,597],{"className":910},[620]," übrig, der ",[796,913,914],{},"verminderte Grundwert",".",[565,917,918,919,1091,1092,1234,1235,1237],{},"Den Faktor ",[569,920,922,952],{"className":921},[572],[569,923,925],{"className":924},[576],[578,926,927],{"xmlns":580},[582,928,929,949],{},[585,930,931,934,937,940,942],{},[588,932,933],{},"q",[726,935,936],{},"=",[644,938,939],{},"1",[726,941,734],{},[943,944,945,947],"mfrac",{},[588,946,565],{},[644,948,646],{},[599,950,951],{"encoding":601},"q = 1 + \\frac{p}{100}",[569,953,955,977,996],{"className":954,"ariaHidden":607},[606],[569,956,958,962,966,970,974],{"className":957},[611],[569,959],{"className":960,"style":961},[615],"height:0.625em;vertical-align:-0.1944em;",[569,963,933],{"className":964,"style":965},[620,621],"margin-right:0.0359em;",[569,967],{"className":968,"style":969},[625],"margin-right:0.2778em;",[569,971,936],{"className":972},[973],"mrel",[569,975],{"className":976,"style":969},[625],[569,978,980,984,987,990,993],{"className":979},[611],[569,981],{"className":982,"style":983},[615],"height:0.7278em;vertical-align:-0.0833em;",[569,985,939],{"className":986},[620],[569,988],{"className":989,"style":767},[625],[569,991,734],{"className":992},[771],[569,994],{"className":995,"style":767},[625],[569,997,999,1003],{"className":998},[611],[569,1000],{"className":1001,"style":1002},[615],"height:1.0925em;vertical-align:-0.345em;",[569,1004,1006,1010,1088],{"className":1005},[620],[569,1007],{"className":1008},[760,1009],"nulldelimiter",[569,1011,1013],{"className":1012},[943],[569,1014,1018,1079],{"className":1015},[1016,1017],"vlist-t","vlist-t2",[569,1019,1022,1074],{"className":1020},[1021],"vlist-r",[569,1023,1027,1048,1059],{"className":1024,"style":1026},[1025],"vlist","height:0.7475em;",[569,1028,1030,1035],{"style":1029},"top:-2.655em;",[569,1031],{"className":1032,"style":1034},[1033],"pstrut","height:3em;",[569,1036,1042],{"className":1037},[1038,1039,1040,1041],"sizing","reset-size6","size3","mtight",[569,1043,1045],{"className":1044},[620,1041],[569,1046,646],{"className":1047},[620,1041],[569,1049,1051,1054],{"style":1050},"top:-3.23em;",[569,1052],{"className":1053,"style":1034},[1033],[569,1055],{"className":1056,"style":1058},[1057],"frac-line","border-bottom-width:0.04em;",[569,1060,1062,1065],{"style":1061},"top:-3.4461em;",[569,1063],{"className":1064,"style":1034},[1033],[569,1066,1068],{"className":1067},[1038,1039,1040,1041],[569,1069,1071],{"className":1070},[620,1041],[569,1072,565],{"className":1073},[620,621,1041],[569,1075,1078],{"className":1076},[1077],"vlist-s","​",[569,1080,1082],{"className":1081},[1021],[569,1083,1086],{"className":1084,"style":1085},[1025],"height:0.345em;",[569,1087],{},[569,1089],{"className":1090},[787,1009]," bzw. ",[569,1093,1095,1121],{"className":1094},[572],[569,1096,1098],{"className":1097},[576],[578,1099,1100],{"xmlns":580},[582,1101,1102,1118],{},[585,1103,1104,1106,1108,1110,1112],{},[588,1105,933],{},[726,1107,936],{},[644,1109,939],{},[726,1111,857],{},[943,1113,1114,1116],{},[588,1115,565],{},[644,1117,646],{},[599,1119,1120],{"encoding":601},"q = 1 - \\frac{p}{100}",[569,1122,1124,1142,1160],{"className":1123,"ariaHidden":607},[606],[569,1125,1127,1130,1133,1136,1139],{"className":1126},[611],[569,1128],{"className":1129,"style":961},[615],[569,1131,933],{"className":1132,"style":965},[620,621],[569,1134],{"className":1135,"style":969},[625],[569,1137,936],{"className":1138},[973],[569,1140],{"className":1141,"style":969},[625],[569,1143,1145,1148,1151,1154,1157],{"className":1144},[611],[569,1146],{"className":1147,"style":983},[615],[569,1149,939],{"className":1150},[620],[569,1152],{"className":1153,"style":767},[625],[569,1155,857],{"className":1156},[771],[569,1158],{"className":1159,"style":767},[625],[569,1161,1163,1166],{"className":1162},[611],[569,1164],{"className":1165,"style":1002},[615],[569,1167,1169,1172,1231],{"className":1168},[620],[569,1170],{"className":1171},[760,1009],[569,1173,1175],{"className":1174},[943],[569,1176,1178,1223],{"className":1177},[1016,1017],[569,1179,1181,1220],{"className":1180},[1021],[569,1182,1184,1198,1206],{"className":1183,"style":1026},[1025],[569,1185,1186,1189],{"style":1029},[569,1187],{"className":1188,"style":1034},[1033],[569,1190,1192],{"className":1191},[1038,1039,1040,1041],[569,1193,1195],{"className":1194},[620,1041],[569,1196,646],{"className":1197},[620,1041],[569,1199,1200,1203],{"style":1050},[569,1201],{"className":1202,"style":1034},[1033],[569,1204],{"className":1205,"style":1058},[1057],[569,1207,1208,1211],{"style":1061},[569,1209],{"className":1210,"style":1034},[1033],[569,1212,1214],{"className":1213},[1038,1039,1040,1041],[569,1215,1217],{"className":1216},[620,1041],[569,1218,565],{"className":1219},[620,621,1041],[569,1221,1078],{"className":1222},[1077],[569,1224,1226],{"className":1225},[1021],[569,1227,1229],{"className":1228,"style":1085},[1025],[569,1230],{},[569,1232],{"className":1233},[787,1009]," nennt man ",[796,1236,550],{}," (bei Zunahme auch Wachstumsfaktor). Mit ihm braucht man nur eine Rechnung statt zwei:",[1239,1240,1241,1356],"ul",{},[1242,1243,1244,1290,1291],"li",{},[569,1245,1247,1268],{"className":1246},[572],[569,1248,1250],{"className":1249},[576],[578,1251,1252],{"xmlns":580},[582,1253,1254,1265],{},[585,1255,1256,1258,1261,1263],{},[726,1257,734],{},[644,1259,1260],{},"8",[591,1262,593],{},[588,1264,597],{"mathvariant":596},[599,1266,1267],{"encoding":601},"+8\\,\\%",[569,1269,1271],{"className":1270,"ariaHidden":607},[606],[569,1272,1274,1278,1281,1284,1287],{"className":1273},[611],[569,1275],{"className":1276,"style":1277},[615],"height:0.8333em;vertical-align:-0.0833em;",[569,1279,734],{"className":1280},[620],[569,1282,1260],{"className":1283},[620],[569,1285],{"className":1286,"style":626},[625],[569,1288,597],{"className":1289},[620],": ",[569,1292,1294,1313],{"className":1293},[572],[569,1295,1297],{"className":1296},[576],[578,1298,1299],{"xmlns":580},[582,1300,1301,1310],{},[585,1302,1303,1305,1307],{},[588,1304,933],{},[726,1306,936],{},[644,1308,1309],{},"1,08",[599,1311,1312],{"encoding":601},"q = 1{,}08",[569,1314,1316,1334],{"className":1315,"ariaHidden":607},[606],[569,1317,1319,1322,1325,1328,1331],{"className":1318},[611],[569,1320],{"className":1321,"style":961},[615],[569,1323,933],{"className":1324,"style":965},[620,621],[569,1326],{"className":1327,"style":969},[625],[569,1329,936],{"className":1330},[973],[569,1332],{"className":1333,"style":969},[625],[569,1335,1337,1341,1344,1352],{"className":1336},[611],[569,1338],{"className":1339,"style":1340},[615],"height:0.8389em;vertical-align:-0.1944em;",[569,1342,939],{"className":1343},[620],[569,1345,1347],{"className":1346},[620],[569,1348,1351],{"className":1349},[1350],"mpunct",",",[569,1353,1355],{"className":1354},[620],"08",[1242,1357,1358,1290,1403],{},[569,1359,1361,1382],{"className":1360},[572],[569,1362,1364],{"className":1363},[576],[578,1365,1366],{"xmlns":580},[582,1367,1368,1379],{},[585,1369,1370,1372,1375,1377],{},[726,1371,857],{},[644,1373,1374],{},"25",[591,1376,593],{},[588,1378,597],{"mathvariant":596},[599,1380,1381],{"encoding":601},"-25\\,\\%",[569,1383,1385],{"className":1384,"ariaHidden":607},[606],[569,1386,1388,1391,1394,1397,1400],{"className":1387},[611],[569,1389],{"className":1390,"style":1277},[615],[569,1392,857],{"className":1393},[620],[569,1395,1374],{"className":1396},[620],[569,1398],{"className":1399,"style":626},[625],[569,1401,597],{"className":1402},[620],[569,1404,1406,1425],{"className":1405},[572],[569,1407,1409],{"className":1408},[576],[578,1410,1411],{"xmlns":580},[582,1412,1413,1422],{},[585,1414,1415,1417,1419],{},[588,1416,933],{},[726,1418,936],{},[644,1420,1421],{},"0,75",[599,1423,1424],{"encoding":601},"q = 0{,}75",[569,1426,1428,1446],{"className":1427,"ariaHidden":607},[606],[569,1429,1431,1434,1437,1440,1443],{"className":1430},[611],[569,1432],{"className":1433,"style":961},[615],[569,1435,933],{"className":1436,"style":965},[620,621],[569,1438],{"className":1439,"style":969},[625],[569,1441,936],{"className":1442},[973],[569,1444],{"className":1445,"style":969},[625],[569,1447,1449,1452,1456,1462],{"className":1448},[611],[569,1450],{"className":1451,"style":1340},[615],[569,1453,1455],{"className":1454},[620],"0",[569,1457,1459],{"className":1458},[620],[569,1460,1351],{"className":1461},[1350],[569,1463,1465],{"className":1464},[620],"75",[565,1467,1468,1469,1290,1497,915],{},"Rückwärts rechnet man durch ",[569,1470,1472,1485],{"className":1471},[572],[569,1473,1475],{"className":1474},[576],[578,1476,1477],{"xmlns":580},[582,1478,1479,1483],{},[585,1480,1481],{},[588,1482,933],{},[599,1484,933],{"encoding":601},[569,1486,1488],{"className":1487,"ariaHidden":607},[606],[569,1489,1491,1494],{"className":1490},[611],[569,1492],{"className":1493,"style":961},[615],[569,1495,933],{"className":1496,"style":965},[620,621],[569,1498,1500,1529],{"className":1499},[572],[569,1501,1503],{"className":1502},[576],[578,1504,1505],{"xmlns":580},[582,1506,1507,1526],{},[585,1508,1509,1512,1514],{},[588,1510,1511],{},"G",[726,1513,936],{},[943,1515,1516,1524],{},[1517,1518,1519,1521],"msub",{},[588,1520,1511],{},[591,1522,1523],{},"neu",[588,1525,933],{},[599,1527,1528],{"encoding":601},"G = \\frac{G_{\\text{neu}}}{q}",[569,1530,1532,1551],{"className":1531,"ariaHidden":607},[606],[569,1533,1535,1539,1542,1545,1548],{"className":1534},[611],[569,1536],{"className":1537,"style":1538},[615],"height:0.6833em;",[569,1540,1511],{"className":1541},[620,621],[569,1543],{"className":1544,"style":969},[625],[569,1546,936],{"className":1547},[973],[569,1549],{"className":1550,"style":969},[625],[569,1552,1554,1558],{"className":1553},[611],[569,1555],{"className":1556,"style":1557},[615],"height:1.3695em;vertical-align:-0.4811em;",[569,1559,1561,1564,1677],{"className":1560},[620],[569,1562],{"className":1563},[760,1009],[569,1565,1567],{"className":1566},[943],[569,1568,1570,1668],{"className":1569},[1016,1017],[569,1571,1573,1665],{"className":1572},[1021],[569,1574,1577,1591,1599],{"className":1575,"style":1576},[1025],"height:0.8884em;",[569,1578,1579,1582],{"style":1029},[569,1580],{"className":1581,"style":1034},[1033],[569,1583,1585],{"className":1584},[1038,1039,1040,1041],[569,1586,1588],{"className":1587},[620,1041],[569,1589,933],{"className":1590,"style":965},[620,621,1041],[569,1592,1593,1596],{"style":1050},[569,1594],{"className":1595,"style":1034},[1033],[569,1597],{"className":1598,"style":1058},[1057],[569,1600,1602,1605],{"style":1601},"top:-3.4101em;",[569,1603],{"className":1604,"style":1034},[1033],[569,1606,1608],{"className":1607},[1038,1039,1040,1041],[569,1609,1611],{"className":1610},[620,1041],[569,1612,1614,1617],{"className":1613},[620,1041],[569,1615,1511],{"className":1616},[620,621,1041],[569,1618,1621],{"className":1619},[1620],"msupsub",[569,1622,1624,1656],{"className":1623},[1016,1017],[569,1625,1627,1653],{"className":1626},[1021],[569,1628,1631],{"className":1629,"style":1630},[1025],"height:0.1645em;",[569,1632,1634,1638],{"style":1633},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[569,1635],{"className":1636,"style":1637},[1033],"height:2.5em;",[569,1639,1643],{"className":1640},[1038,1641,1642,1041],"reset-size3","size1",[569,1644,1646],{"className":1645},[620,1041],[569,1647,1650],{"className":1648},[620,1649,1041],"text",[569,1651,1523],{"className":1652},[620,1041],[569,1654,1078],{"className":1655},[1077],[569,1657,1659],{"className":1658},[1021],[569,1660,1663],{"className":1661,"style":1662},[1025],"height:0.143em;",[569,1664],{},[569,1666,1078],{"className":1667},[1077],[569,1669,1671],{"className":1670},[1021],[569,1672,1675],{"className":1673,"style":1674},[1025],"height:0.4811em;",[569,1676],{},[569,1678],{"className":1679},[787,1009],[565,1681,1682,1683,1721,1722,1776],{},"Eine Abnahme um mehr als ",[569,1684,1686,1703],{"className":1685},[572],[569,1687,1689],{"className":1688},[576],[578,1690,1691],{"xmlns":580},[582,1692,1693,1701],{},[585,1694,1695,1697,1699],{},[644,1696,646],{},[591,1698,593],{},[588,1700,597],{"mathvariant":596},[599,1702,653],{"encoding":601},[569,1704,1706],{"className":1705,"ariaHidden":607},[606],[569,1707,1709,1712,1715,1718],{"className":1708},[611],[569,1710],{"className":1711,"style":663},[615],[569,1713,646],{"className":1714},[620],[569,1716],{"className":1717,"style":626},[625],[569,1719,597],{"className":1720},[620]," ergibt keinen Sinn, deshalb muss bei einer Abnahme zusätzlich ",[569,1723,1725,1744],{"className":1724},[572],[569,1726,1728],{"className":1727},[576],[578,1729,1730],{"xmlns":580},[582,1731,1732,1741],{},[585,1733,1734,1736,1739],{},[588,1735,565],{},[726,1737,1738],{},"≤",[644,1740,646],{},[599,1742,1743],{"encoding":601},"p \\leq 100",[569,1745,1747,1766],{"className":1746,"ariaHidden":607},[606],[569,1748,1750,1754,1757,1760,1763],{"className":1749},[611],[569,1751],{"className":1752,"style":1753},[615],"height:0.8304em;vertical-align:-0.1944em;",[569,1755,565],{"className":1756},[620,621],[569,1758],{"className":1759,"style":969},[625],[569,1761,1738],{"className":1762},[973],[569,1764],{"className":1765,"style":969},[625],[569,1767,1769,1773],{"className":1768},[611],[569,1770],{"className":1771,"style":1772},[615],"height:0.6444em;",[569,1774,646],{"className":1775},[620]," gelten.",[560,1778,1780],{"id":1779},"beispiele","Beispiele",[565,1782,1783,1784,1813,1814,1853],{},"Eine Miete von ",[569,1785,1787,1801],{"className":1786},[572],[569,1788,1790],{"className":1789},[576],[578,1791,1792],{"xmlns":580},[582,1793,1794,1799],{},[585,1795,1796],{},[644,1797,1798],{},"250",[599,1800,1798],{"encoding":601},[569,1802,1804],{"className":1803,"ariaHidden":607},[606],[569,1805,1807,1810],{"className":1806},[611],[569,1808],{"className":1809,"style":1772},[615],[569,1811,1798],{"className":1812},[620]," € steigt um ",[569,1815,1817,1835],{"className":1816},[572],[569,1818,1820],{"className":1819},[576],[578,1821,1822],{"xmlns":580},[582,1823,1824,1832],{},[585,1825,1826,1828,1830],{},[644,1827,1260],{},[591,1829,593],{},[588,1831,597],{"mathvariant":596},[599,1833,1834],{"encoding":601},"8\\,\\%",[569,1836,1838],{"className":1837,"ariaHidden":607},[606],[569,1839,1841,1844,1847,1850],{"className":1840},[611],[569,1842],{"className":1843,"style":663},[615],[569,1845,1260],{"className":1846},[620],[569,1848],{"className":1849,"style":626},[625],[569,1851,597],{"className":1852},[620],":",[569,1855,1858],{"className":1856},[1857],"katex-display",[569,1859,1861,1894],{"className":1860},[572],[569,1862,1864],{"className":1863},[576],[578,1865,1867],{"xmlns":580,"display":1866},"block",[582,1868,1869,1891],{},[585,1870,1871,1877,1879,1881,1884,1886,1888],{},[1517,1872,1873,1875],{},[588,1874,1511],{},[591,1876,1523],{},[726,1878,936],{},[644,1880,1798],{},[726,1882,1883],{},"⋅",[644,1885,1309],{},[726,1887,936],{},[644,1889,1890],{},"270",[599,1892,1893],{"encoding":601},"G_{\\text{neu}} = 250 \\cdot 1{,}08 = 270",[569,1895,1897,1963,1981,2008],{"className":1896,"ariaHidden":607},[606],[569,1898,1900,1904,1954,1957,1960],{"className":1899},[611],[569,1901],{"className":1902,"style":1903},[615],"height:0.8333em;vertical-align:-0.15em;",[569,1905,1907,1910],{"className":1906},[620],[569,1908,1511],{"className":1909},[620,621],[569,1911,1913],{"className":1912},[1620],[569,1914,1916,1945],{"className":1915},[1016,1017],[569,1917,1919,1942],{"className":1918},[1021],[569,1920,1923],{"className":1921,"style":1922},[1025],"height:0.1514em;",[569,1924,1926,1930],{"style":1925},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[569,1927],{"className":1928,"style":1929},[1033],"height:2.7em;",[569,1931,1933],{"className":1932},[1038,1039,1040,1041],[569,1934,1936],{"className":1935},[620,1041],[569,1937,1939],{"className":1938},[620,1649,1041],[569,1940,1523],{"className":1941},[620,1041],[569,1943,1078],{"className":1944},[1077],[569,1946,1948],{"className":1947},[1021],[569,1949,1952],{"className":1950,"style":1951},[1025],"height:0.15em;",[569,1953],{},[569,1955],{"className":1956,"style":969},[625],[569,1958,936],{"className":1959},[973],[569,1961],{"className":1962,"style":969},[625],[569,1964,1966,1969,1972,1975,1978],{"className":1965},[611],[569,1967],{"className":1968,"style":1772},[615],[569,1970,1798],{"className":1971},[620],[569,1973],{"className":1974,"style":767},[625],[569,1976,1883],{"className":1977},[771],[569,1979],{"className":1980,"style":767},[625],[569,1982,1984,1987,1990,1996,1999,2002,2005],{"className":1983},[611],[569,1985],{"className":1986,"style":1340},[615],[569,1988,939],{"className":1989},[620],[569,1991,1993],{"className":1992},[620],[569,1994,1351],{"className":1995},[1350],[569,1997,1355],{"className":1998},[620],[569,2000],{"className":2001,"style":969},[625],[569,2003,936],{"className":2004},[973],[569,2006],{"className":2007,"style":969},[625],[569,2009,2011,2014],{"className":2010},[611],[569,2012],{"className":2013,"style":1772},[615],[569,2015,1890],{"className":2016},[620],[565,2018,2019,2020,2049,2050,2089],{},"Eine Jacke kostet ",[569,2021,2023,2037],{"className":2022},[572],[569,2024,2026],{"className":2025},[576],[578,2027,2028],{"xmlns":580},[582,2029,2030,2035],{},[585,2031,2032],{},[644,2033,2034],{},"60",[599,2036,2034],{"encoding":601},[569,2038,2040],{"className":2039,"ariaHidden":607},[606],[569,2041,2043,2046],{"className":2042},[611],[569,2044],{"className":2045,"style":1772},[615],[569,2047,2034],{"className":2048},[620]," €, im Schlussverkauf gibt es ",[569,2051,2053,2071],{"className":2052},[572],[569,2054,2056],{"className":2055},[576],[578,2057,2058],{"xmlns":580},[582,2059,2060,2068],{},[585,2061,2062,2064,2066],{},[644,2063,1374],{},[591,2065,593],{},[588,2067,597],{"mathvariant":596},[599,2069,2070],{"encoding":601},"25\\,\\%",[569,2072,2074],{"className":2073,"ariaHidden":607},[606],[569,2075,2077,2080,2083,2086],{"className":2076},[611],[569,2078],{"className":2079,"style":663},[615],[569,2081,1374],{"className":2082},[620],[569,2084],{"className":2085,"style":626},[625],[569,2087,597],{"className":2088},[620]," Rabatt:",[569,2091,2093],{"className":2092},[1857],[569,2094,2096,2149],{"className":2095},[572],[569,2097,2099],{"className":2098},[576],[578,2100,2101],{"xmlns":580,"display":1866},[582,2102,2103,2146],{},[585,2104,2105,2111,2113,2115,2117,2133,2135,2137,2139,2141,2143],{},[1517,2106,2107,2109],{},[588,2108,1511],{},[591,2110,1523],{},[726,2112,936],{},[644,2114,2034],{},[726,2116,1883],{},[585,2118,2119,2121,2123,2125,2131],{},[726,2120,729],{"fence":607},[644,2122,939],{},[726,2124,857],{},[943,2126,2127,2129],{},[644,2128,1374],{},[644,2130,646],{},[726,2132,739],{"fence":607},[726,2134,936],{},[644,2136,2034],{},[726,2138,1883],{},[644,2140,1421],{},[726,2142,936],{},[644,2144,2145],{},"45",[599,2147,2148],{"encoding":601},"G_{\\text{neu}} = 60 \\cdot \\left(1 - \\frac{25}{100}\\right) = 60 \\cdot 0{,}75 = 45",[569,2150,2152,2213,2231,2344,2362,2389],{"className":2151,"ariaHidden":607},[606],[569,2153,2155,2158,2204,2207,2210],{"className":2154},[611],[569,2156],{"className":2157,"style":1903},[615],[569,2159,2161,2164],{"className":2160},[620],[569,2162,1511],{"className":2163},[620,621],[569,2165,2167],{"className":2166},[1620],[569,2168,2170,2196],{"className":2169},[1016,1017],[569,2171,2173,2193],{"className":2172},[1021],[569,2174,2176],{"className":2175,"style":1922},[1025],[569,2177,2178,2181],{"style":1925},[569,2179],{"className":2180,"style":1929},[1033],[569,2182,2184],{"className":2183},[1038,1039,1040,1041],[569,2185,2187],{"className":2186},[620,1041],[569,2188,2190],{"className":2189},[620,1649,1041],[569,2191,1523],{"className":2192},[620,1041],[569,2194,1078],{"className":2195},[1077],[569,2197,2199],{"className":2198},[1021],[569,2200,2202],{"className":2201,"style":1951},[1025],[569,2203],{},[569,2205],{"className":2206,"style":969},[625],[569,2208,936],{"className":2209},[973],[569,2211],{"className":2212,"style":969},[625],[569,2214,2216,2219,2222,2225,2228],{"className":2215},[611],[569,2217],{"className":2218,"style":1772},[615],[569,2220,2034],{"className":2221},[620],[569,2223],{"className":2224,"style":767},[625],[569,2226,1883],{"className":2227},[771],[569,2229],{"className":2230,"style":767},[625],[569,2232,2234,2238,2335,2338,2341],{"className":2233},[611],[569,2235],{"className":2236,"style":2237},[615],"height:2.4em;vertical-align:-0.95em;",[569,2239,2242,2251,2254,2257,2260,2263,2329],{"className":2240},[2241],"minner",[569,2243,2247],{"className":2244,"style":2246},[760,2245],"delimcenter","top:0em;",[569,2248,729],{"className":2249},[2250,1040],"delimsizing",[569,2252,939],{"className":2253},[620],[569,2255],{"className":2256,"style":767},[625],[569,2258,857],{"className":2259},[771],[569,2261],{"className":2262,"style":767},[625],[569,2264,2266,2269,2326],{"className":2265},[620],[569,2267],{"className":2268},[760,1009],[569,2270,2272],{"className":2271},[943],[569,2273,2275,2317],{"className":2274},[1016,1017],[569,2276,2278,2314],{"className":2277},[1021],[569,2279,2282,2294,2302],{"className":2280,"style":2281},[1025],"height:1.3214em;",[569,2283,2285,2288],{"style":2284},"top:-2.314em;",[569,2286],{"className":2287,"style":1034},[1033],[569,2289,2291],{"className":2290},[620],[569,2292,646],{"className":2293},[620],[569,2295,2296,2299],{"style":1050},[569,2297],{"className":2298,"style":1034},[1033],[569,2300],{"className":2301,"style":1058},[1057],[569,2303,2305,2308],{"style":2304},"top:-3.677em;",[569,2306],{"className":2307,"style":1034},[1033],[569,2309,2311],{"className":2310},[620],[569,2312,1374],{"className":2313},[620],[569,2315,1078],{"className":2316},[1077],[569,2318,2320],{"className":2319},[1021],[569,2321,2324],{"className":2322,"style":2323},[1025],"height:0.686em;",[569,2325],{},[569,2327],{"className":2328},[787,1009],[569,2330,2332],{"className":2331,"style":2246},[787,2245],[569,2333,739],{"className":2334},[2250,1040],[569,2336],{"className":2337,"style":969},[625],[569,2339,936],{"className":2340},[973],[569,2342],{"className":2343,"style":969},[625],[569,2345,2347,2350,2353,2356,2359],{"className":2346},[611],[569,2348],{"className":2349,"style":1772},[615],[569,2351,2034],{"className":2352},[620],[569,2354],{"className":2355,"style":767},[625],[569,2357,1883],{"className":2358},[771],[569,2360],{"className":2361,"style":767},[625],[569,2363,2365,2368,2371,2377,2380,2383,2386],{"className":2364},[611],[569,2366],{"className":2367,"style":1340},[615],[569,2369,1455],{"className":2370},[620],[569,2372,2374],{"className":2373},[620],[569,2375,1351],{"className":2376},[1350],[569,2378,1465],{"className":2379},[620],[569,2381],{"className":2382,"style":969},[625],[569,2384,936],{"className":2385},[973],[569,2387],{"className":2388,"style":969},[625],[569,2390,2392,2395],{"className":2391},[611],[569,2393],{"className":2394,"style":1772},[615],[569,2396,2145],{"className":2397},[620],[565,2399,2400,2401,2441,2442,2471],{},"Nach einer Preiserhöhung um ",[569,2402,2404,2423],{"className":2403},[572],[569,2405,2407],{"className":2406},[576],[578,2408,2409],{"xmlns":580},[582,2410,2411,2420],{},[585,2412,2413,2416,2418],{},[644,2414,2415],{},"20",[591,2417,593],{},[588,2419,597],{"mathvariant":596},[599,2421,2422],{"encoding":601},"20\\,\\%",[569,2424,2426],{"className":2425,"ariaHidden":607},[606],[569,2427,2429,2432,2435,2438],{"className":2428},[611],[569,2430],{"className":2431,"style":663},[615],[569,2433,2415],{"className":2434},[620],[569,2436],{"className":2437,"style":626},[625],[569,2439,597],{"className":2440},[620]," kostet ein Ticket ",[569,2443,2445,2459],{"className":2444},[572],[569,2446,2448],{"className":2447},[576],[578,2449,2450],{"xmlns":580},[582,2451,2452,2457],{},[585,2453,2454],{},[644,2455,2456],{},"72",[599,2458,2456],{"encoding":601},[569,2460,2462],{"className":2461,"ariaHidden":607},[606],[569,2463,2465,2468],{"className":2464},[611],[569,2466],{"className":2467,"style":1772},[615],[569,2469,2456],{"className":2470},[620]," €. Vorher kostete es",[569,2473,2475],{"className":2474},[1857],[569,2476,2478,2505],{"className":2477},[572],[569,2479,2481],{"className":2480},[576],[578,2482,2483],{"xmlns":580,"display":1866},[582,2484,2485,2502],{},[585,2486,2487,2489,2491,2498,2500],{},[588,2488,1511],{},[726,2490,936],{},[943,2492,2493,2495],{},[644,2494,2456],{},[644,2496,2497],{},"1,2",[726,2499,936],{},[644,2501,2034],{},[599,2503,2504],{"encoding":601},"G = \\frac{72}{1{,}2} = 60",[569,2506,2508,2526,2615],{"className":2507,"ariaHidden":607},[606],[569,2509,2511,2514,2517,2520,2523],{"className":2510},[611],[569,2512],{"className":2513,"style":1538},[615],[569,2515,1511],{"className":2516},[620,621],[569,2518],{"className":2519,"style":969},[625],[569,2521,936],{"className":2522},[973],[569,2524],{"className":2525,"style":969},[625],[569,2527,2529,2533,2606,2609,2612],{"className":2528},[611],[569,2530],{"className":2531,"style":2532},[615],"height:2.2019em;vertical-align:-0.8804em;",[569,2534,2536,2539,2603],{"className":2535},[620],[569,2537],{"className":2538},[760,1009],[569,2540,2542],{"className":2541},[943],[569,2543,2545,2594],{"className":2544},[1016,1017],[569,2546,2548,2591],{"className":2547},[1021],[569,2549,2551,2572,2580],{"className":2550,"style":2281},[1025],[569,2552,2553,2556],{"style":2284},[569,2554],{"className":2555,"style":1034},[1033],[569,2557,2559,2562,2568],{"className":2558},[620],[569,2560,939],{"className":2561},[620],[569,2563,2565],{"className":2564},[620],[569,2566,1351],{"className":2567},[1350],[569,2569,2571],{"className":2570},[620],"2",[569,2573,2574,2577],{"style":1050},[569,2575],{"className":2576,"style":1034},[1033],[569,2578],{"className":2579,"style":1058},[1057],[569,2581,2582,2585],{"style":2304},[569,2583],{"className":2584,"style":1034},[1033],[569,2586,2588],{"className":2587},[620],[569,2589,2456],{"className":2590},[620],[569,2592,1078],{"className":2593},[1077],[569,2595,2597],{"className":2596},[1021],[569,2598,2601],{"className":2599,"style":2600},[1025],"height:0.8804em;",[569,2602],{},[569,2604],{"className":2605},[787,1009],[569,2607],{"className":2608,"style":969},[625],[569,2610,936],{"className":2611},[973],[569,2613],{"className":2614,"style":969},[625],[569,2616,2618,2621],{"className":2617},[611],[569,2619],{"className":2620,"style":1772},[615],[569,2622,2034],{"className":2623},[620],[565,2625,2626,2627,2655],{},"also ",[569,2628,2630,2643],{"className":2629},[572],[569,2631,2633],{"className":2632},[576],[578,2634,2635],{"xmlns":580},[582,2636,2637,2641],{},[585,2638,2639],{},[644,2640,2034],{},[599,2642,2034],{"encoding":601},[569,2644,2646],{"className":2645,"ariaHidden":607},[606],[569,2647,2649,2652],{"className":2648},[611],[569,2650],{"className":2651,"style":1772},[615],[569,2653,2034],{"className":2654},[620]," €.",[560,2657,2659],{"id":2658},"typische-fehler","Typische Fehler",[1239,2661,2662,2858,3098],{},[1242,2663,2664,2665,2693,2694,2732,2733,2771,2772,2775,2776,915],{},"Beim Zurückrechnen den Prozentsatz abziehen: ",[569,2666,2668,2681],{"className":2667},[572],[569,2669,2671],{"className":2670},[576],[578,2672,2673],{"xmlns":580},[582,2674,2675,2679],{},[585,2676,2677],{},[644,2678,2456],{},[599,2680,2456],{"encoding":601},[569,2682,2684],{"className":2683,"ariaHidden":607},[606],[569,2685,2687,2690],{"className":2686},[611],[569,2688],{"className":2689,"style":1772},[615],[569,2691,2456],{"className":2692},[620]," € minus ",[569,2695,2697,2714],{"className":2696},[572],[569,2698,2700],{"className":2699},[576],[578,2701,2702],{"xmlns":580},[582,2703,2704,2712],{},[585,2705,2706,2708,2710],{},[644,2707,2415],{},[591,2709,593],{},[588,2711,597],{"mathvariant":596},[599,2713,2422],{"encoding":601},[569,2715,2717],{"className":2716,"ariaHidden":607},[606],[569,2718,2720,2723,2726,2729],{"className":2719},[611],[569,2721],{"className":2722,"style":663},[615],[569,2724,2415],{"className":2725},[620],[569,2727],{"className":2728,"style":626},[625],[569,2730,597],{"className":2731},[620]," ergibt nicht den alten Preis, weil sich die ",[569,2734,2736,2753],{"className":2735},[572],[569,2737,2739],{"className":2738},[576],[578,2740,2741],{"xmlns":580},[582,2742,2743,2751],{},[585,2744,2745,2747,2749],{},[644,2746,2415],{},[591,2748,593],{},[588,2750,597],{"mathvariant":596},[599,2752,2422],{"encoding":601},[569,2754,2756],{"className":2755,"ariaHidden":607},[606],[569,2757,2759,2762,2765,2768],{"className":2758},[611],[569,2760],{"className":2761,"style":663},[615],[569,2763,2415],{"className":2764},[620],[569,2766],{"className":2767,"style":626},[625],[569,2769,597],{"className":2770},[620]," auf den ",[796,2773,2774],{},"alten"," Preis beziehen. Richtig ist ",[569,2777,2779,2801],{"className":2778},[572],[569,2780,2782],{"className":2781},[576],[578,2783,2784],{"xmlns":580},[582,2785,2786,2798],{},[585,2787,2788,2790,2792,2794,2796],{},[644,2789,2456],{},[726,2791,1853],{},[644,2793,2497],{},[726,2795,936],{},[644,2797,2034],{},[599,2799,2800],{"encoding":601},"72 : 1{,}2 = 60",[569,2802,2804,2822,2849],{"className":2803,"ariaHidden":607},[606],[569,2805,2807,2810,2813,2816,2819],{"className":2806},[611],[569,2808],{"className":2809,"style":1772},[615],[569,2811,2456],{"className":2812},[620],[569,2814],{"className":2815,"style":969},[625],[569,2817,1853],{"className":2818},[973],[569,2820],{"className":2821,"style":969},[625],[569,2823,2825,2828,2831,2837,2840,2843,2846],{"className":2824},[611],[569,2826],{"className":2827,"style":1340},[615],[569,2829,939],{"className":2830},[620],[569,2832,2834],{"className":2833},[620],[569,2835,1351],{"className":2836},[1350],[569,2838,2571],{"className":2839},[620],[569,2841],{"className":2842,"style":969},[625],[569,2844,936],{"className":2845},[973],[569,2847],{"className":2848,"style":969},[625],[569,2850,2852,2855],{"className":2851},[611],[569,2853],{"className":2854,"style":1772},[615],[569,2856,2034],{"className":2857},[620],[1242,2859,2860,2861,2906,2907,2951,2952,2980,2981,915],{},"Prozente einfach addieren: ",[569,2862,2864,2885],{"className":2863},[572],[569,2865,2867],{"className":2866},[576],[578,2868,2869],{"xmlns":580},[582,2870,2871,2882],{},[585,2872,2873,2875,2878,2880],{},[726,2874,734],{},[644,2876,2877],{},"10",[591,2879,593],{},[588,2881,597],{"mathvariant":596},[599,2883,2884],{"encoding":601},"+10\\,\\%",[569,2886,2888],{"className":2887,"ariaHidden":607},[606],[569,2889,2891,2894,2897,2900,2903],{"className":2890},[611],[569,2892],{"className":2893,"style":1277},[615],[569,2895,734],{"className":2896},[620],[569,2898,2877],{"className":2899},[620],[569,2901],{"className":2902,"style":626},[625],[569,2904,597],{"className":2905},[620]," und danach ",[569,2908,2910,2930],{"className":2909},[572],[569,2911,2913],{"className":2912},[576],[578,2914,2915],{"xmlns":580},[582,2916,2917,2927],{},[585,2918,2919,2921,2923,2925],{},[726,2920,857],{},[644,2922,2877],{},[591,2924,593],{},[588,2926,597],{"mathvariant":596},[599,2928,2929],{"encoding":601},"-10\\,\\%",[569,2931,2933],{"className":2932,"ariaHidden":607},[606],[569,2934,2936,2939,2942,2945,2948],{"className":2935},[611],[569,2937],{"className":2938,"style":1277},[615],[569,2940,857],{"className":2941},[620],[569,2943,2877],{"className":2944},[620],[569,2946],{"className":2947,"style":626},[625],[569,2949,597],{"className":2950},[620]," führen nicht zurück zum Start. Aus ",[569,2953,2955,2968],{"className":2954},[572],[569,2956,2958],{"className":2957},[576],[578,2959,2960],{"xmlns":580},[582,2961,2962,2966],{},[585,2963,2964],{},[644,2965,646],{},[599,2967,646],{"encoding":601},[569,2969,2971],{"className":2970,"ariaHidden":607},[606],[569,2972,2974,2977],{"className":2973},[611],[569,2975],{"className":2976,"style":1772},[615],[569,2978,646],{"className":2979},[620]," wird ",[569,2982,2984,3013],{"className":2983},[572],[569,2985,2987],{"className":2986},[576],[578,2988,2989],{"xmlns":580},[582,2990,2991,3010],{},[585,2992,2993,2995,2997,3000,3002,3005,3007],{},[644,2994,646],{},[726,2996,1883],{},[644,2998,2999],{},"1,1",[726,3001,1883],{},[644,3003,3004],{},"0,9",[726,3006,936],{},[644,3008,3009],{},"99",[599,3011,3012],{"encoding":601},"100 \\cdot 1{,}1 \\cdot 0{,}9 = 99",[569,3014,3016,3034,3061,3089],{"className":3015,"ariaHidden":607},[606],[569,3017,3019,3022,3025,3028,3031],{"className":3018},[611],[569,3020],{"className":3021,"style":1772},[615],[569,3023,646],{"className":3024},[620],[569,3026],{"className":3027,"style":767},[625],[569,3029,1883],{"className":3030},[771],[569,3032],{"className":3033,"style":767},[625],[569,3035,3037,3040,3043,3049,3052,3055,3058],{"className":3036},[611],[569,3038],{"className":3039,"style":1340},[615],[569,3041,939],{"className":3042},[620],[569,3044,3046],{"className":3045},[620],[569,3047,1351],{"className":3048},[1350],[569,3050,939],{"className":3051},[620],[569,3053],{"className":3054,"style":767},[625],[569,3056,1883],{"className":3057},[771],[569,3059],{"className":3060,"style":767},[625],[569,3062,3064,3067,3070,3076,3080,3083,3086],{"className":3063},[611],[569,3065],{"className":3066,"style":1340},[615],[569,3068,1455],{"className":3069},[620],[569,3071,3073],{"className":3072},[620],[569,3074,1351],{"className":3075},[1350],[569,3077,3079],{"className":3078},[620],"9",[569,3081],{"className":3082,"style":969},[625],[569,3084,936],{"className":3085},[973],[569,3087],{"className":3088,"style":969},[625],[569,3090,3092,3095],{"className":3091},[611],[569,3093],{"className":3094,"style":1772},[615],[569,3096,3009],{"className":3097},[620],[1242,3099,3100,3101,3144,3145,3204,3205,915],{},"Den Faktor falsch bilden: Bei ",[569,3102,3104,3123],{"className":3103},[572],[569,3105,3107],{"className":3106},[576],[578,3108,3109],{"xmlns":580},[582,3110,3111,3121],{},[585,3112,3113,3115,3117,3119],{},[726,3114,857],{},[644,3116,1374],{},[591,3118,593],{},[588,3120,597],{"mathvariant":596},[599,3122,1381],{"encoding":601},[569,3124,3126],{"className":3125,"ariaHidden":607},[606],[569,3127,3129,3132,3135,3138,3141],{"className":3128},[611],[569,3130],{"className":3131,"style":1277},[615],[569,3133,857],{"className":3134},[620],[569,3136,1374],{"className":3137},[620],[569,3139],{"className":3140,"style":626},[625],[569,3142,597],{"className":3143},[620]," ist ",[569,3146,3148,3165],{"className":3147},[572],[569,3149,3151],{"className":3150},[576],[578,3152,3153],{"xmlns":580},[582,3154,3155,3163],{},[585,3156,3157,3159,3161],{},[588,3158,933],{},[726,3160,936],{},[644,3162,1421],{},[599,3164,1424],{"encoding":601},[569,3166,3168,3186],{"className":3167,"ariaHidden":607},[606],[569,3169,3171,3174,3177,3180,3183],{"className":3170},[611],[569,3172],{"className":3173,"style":961},[615],[569,3175,933],{"className":3176,"style":965},[620,621],[569,3178],{"className":3179,"style":969},[625],[569,3181,936],{"className":3182},[973],[569,3184],{"className":3185,"style":969},[625],[569,3187,3189,3192,3195,3201],{"className":3188},[611],[569,3190],{"className":3191,"style":1340},[615],[569,3193,1455],{"className":3194},[620],[569,3196,3198],{"className":3197},[620],[569,3199,1351],{"className":3200},[1350],[569,3202,1465],{"className":3203},[620],", nicht ",[569,3206,3208,3223],{"className":3207},[572],[569,3209,3211],{"className":3210},[576],[578,3212,3213],{"xmlns":580},[582,3214,3215,3220],{},[585,3216,3217],{},[644,3218,3219],{},"0,25",[599,3221,3222],{"encoding":601},"0{,}25",[569,3224,3226],{"className":3225,"ariaHidden":607},[606],[569,3227,3229,3232,3235,3241],{"className":3228},[611],[569,3230],{"className":3231,"style":1340},[615],[569,3233,1455],{"className":3234},[620],[569,3236,3238],{"className":3237},[620],[569,3239,1351],{"className":3240},[1350],[569,3242,1374],{"className":3243},[620],{"title":3245,"searchDepth":3246,"depth":3246,"links":3247},"",2,[3248,3249,3250],{"id":562,"depth":3246,"text":563},{"id":1779,"depth":3246,"text":1780},{"id":2658,"depth":3246,"text":2659},[3252,3255,3258,3262,3264,3267,3268,3270],{"lhs":3253,"rhs":3254},"G + G*p\u002F100","G*(1 + p\u002F100)",{"lhs":3256,"rhs":3257},"G - G*p\u002F100","G*(1 - p\u002F100)",{"lhs":3254,"rhs":1890,"where":3259},{"G":3260,"p":3261},250,8,{"lhs":3263,"rhs":1890},"250*1.08",{"lhs":3265,"rhs":3266},"60*(1 - 25\u002F100)","60*0.75",{"lhs":3266,"rhs":2145},{"lhs":3269,"rhs":2034},"72\u002F1.2",{"lhs":3271,"rhs":3009},"100*1.1*0.9","p \\geq 0","\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>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p \\geq 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:0.8304em;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:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","change-factor","G_{\\text{neu}} = G \\cdot \\left(1 \\pm \\frac{p}{100}\\right)","\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>G\u003C\u002Fmi>\u003Cmtext>neu\u003C\u002Fmtext>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>G\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>±\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>100\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">G_{\\text{neu}} = G \\cdot \\left(1 \\pm \\frac{p}{100}\\right)\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\">G\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:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord text mtight\">\u003Cspan class=\"mord mtight\">neu\u003C\u002Fspan>\u003C\u002Fspan>\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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">G\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:1.836em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size2\">(\u003C\u002Fspan>\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>\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>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size2\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","middle",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Farithmetic\u002Faenderungsfaktor",[],[3285,3286,3287,3288],"percentage-change","gross-price","base-value","compound-interest",{"title":548,"description":3245},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Faenderungsfaktor","Ein Wert, der um p % steigt oder sinkt, wird mit dem Änderungsfaktor 1 ± p\u002F100 multipliziert.",[3293,3294,3295,3296,3297],"prozent","änderungsfaktor","wachstumsfaktor","rabatt","preiserhöhung",[3299,3303,3306],{"symbol":3300,"meaning":3301,"symbolHtml":3302},"G_{\\text{neu}}","vermehrter oder verminderter Grundwert, der Wert nach der Änderung","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>G\u003C\u002Fmi>\u003Cmtext>neu\u003C\u002Fmtext>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">G_{\\text{neu}}\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\">G\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:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord text mtight\">\u003Cspan class=\"mord mtight\">neu\u003C\u002Fspan>\u003C\u002Fspan>\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":1511,"meaning":3304,"symbolHtml":3305},"ursprünglicher Grundwert","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>G\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">G\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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">G\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":565,"meaning":3307,"symbolHtml":3308},"Prozentsatz der Zunahme (+) oder Abnahme (−) als Zahl","\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>","uQGeoXmlOKZ7UEtOsvTxSOg5COBJLB49mNvimsokNUc",[3311,3314,3317,3320],{"stem":3312,"title":3313,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fbruttopreis","Bruttopreis mit Mehrwertsteuer",{"stem":3315,"title":3316,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fgrundwert","Grundwert",{"stem":3318,"title":3319,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fprozentuale-veraenderung","Prozentuale Veränderung",{"stem":3321,"title":3322,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fzinseszins","Zinseszins",1793824260368]