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Pro Zeitraum gibt es dann den Anteil ",[574,575,578,614],"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",[587,588,589,609],"semantics",{},[590,591,592,601,605],"mrow",{},[593,594,595,598],"mfrac",{},[596,597,565],"mi",{},[596,599,600],{},"m",[602,603,604],"mtext",{}," ",[596,606,608],{"mathvariant":607},"normal","%",[610,611,613],"annotation",{"encoding":612},"application\u002Fx-tex","\\frac{p}{m}\\,\\%",[574,615,619],{"className":616,"ariaHidden":618},[617],"katex-html","true",[574,620,623,628,720,725],{"className":621},[622],"base",[574,624],{"className":625,"style":627},[626],"strut","height:1.095em;vertical-align:-0.345em;",[574,629,632,637,716],{"className":630},[631],"mord",[574,633],{"className":634},[635,636],"mopen","nulldelimiter",[574,638,640],{"className":639},[593],[574,641,645,707],{"className":642},[643,644],"vlist-t","vlist-t2",[574,646,649,702],{"className":647},[648],"vlist-r",[574,650,654,676,687],{"className":651,"style":653},[652],"vlist","height:0.7475em;",[574,655,657,662],{"style":656},"top:-2.655em;",[574,658],{"className":659,"style":661},[660],"pstrut","height:3em;",[574,663,669],{"className":664},[665,666,667,668],"sizing","reset-size6","size3","mtight",[574,670,672],{"className":671},[631,668],[574,673,600],{"className":674},[631,675,668],"mathnormal",[574,677,679,682],{"style":678},"top:-3.23em;",[574,680],{"className":681,"style":661},[660],[574,683],{"className":684,"style":686},[685],"frac-line","border-bottom-width:0.04em;",[574,688,690,693],{"style":689},"top:-3.4461em;",[574,691],{"className":692,"style":661},[660],[574,694,696],{"className":695},[665,666,667,668],[574,697,699],{"className":698},[631,668],[574,700,565],{"className":701},[631,675,668],[574,703,706],{"className":704},[705],"vlist-s","​",[574,708,710],{"className":709},[648],[574,711,714],{"className":712,"style":713},[652],"height:0.345em;",[574,715],{},[574,717],{"className":718},[719,636],"mclose",[574,721],{"className":722,"style":724},[723],"mspace","margin-right:0.1667em;",[574,726,608],{"className":727},[631],". Weil die Zinsen schon im Laufe des Jahres mitverzinst werden, wächst das Kapital etwas stärker, als der Nominalzins vermuten lässt.",[565,730,731,732,735],{},"Der ",[569,733,734],{},"effektive Jahreszins"," ist der Zinssatz, der bei einer einzigen Gutschrift pro Jahr denselben Endbetrag liefern würde. Mit ihm kann man Angebote mit unterschiedlicher Gutschriftshäufigkeit fair vergleichen.",[737,738,739,803],"ul",{},[740,741,742,743,802],"li",{},"Bei ",[574,744,746,768],{"className":745},[577],[574,747,749],{"className":748},[581],[583,750,751],{"xmlns":585},[587,752,753,765],{},[590,754,755,757,761],{},[596,756,600],{},[758,759,760],"mo",{},"=",[762,763,764],"mn",{},"1",[610,766,767],{"encoding":612},"m = 1",[574,769,771,792],{"className":770,"ariaHidden":618},[617],[574,772,774,778,781,785,789],{"className":773},[622],[574,775],{"className":776,"style":777},[626],"height:0.4306em;",[574,779,600],{"className":780},[631,675],[574,782],{"className":783,"style":784},[723],"margin-right:0.2778em;",[574,786,760],{"className":787},[788],"mrel",[574,790],{"className":791,"style":784},[723],[574,793,795,799],{"className":794},[622],[574,796],{"className":797,"style":798},[626],"height:0.6444em;",[574,800,764],{"className":801},[631]," stimmen Nominal- und Effektivzins überein.",[740,804,805,806,834],{},"Je größer ",[574,807,809,822],{"className":808},[577],[574,810,812],{"className":811},[581],[583,813,814],{"xmlns":585},[587,815,816,820],{},[590,817,818],{},[596,819,600],{},[610,821,600],{"encoding":612},[574,823,825],{"className":824,"ariaHidden":618},[617],[574,826,828,831],{"className":827},[622],[574,829],{"className":830,"style":777},[626],[574,832,600],{"className":833},[631,675],", desto größer der Effektivzins. Er steigt aber nicht beliebig, sondern nähert sich der stetigen Verzinsung.",[565,836,837],{},"Hinweis: Bei Verbraucherkrediten ist der gesetzlich vorgeschriebene „effektive Jahreszins“ weiter gefasst. Er enthält neben der Zinsgutschrift auch Gebühren und andere Kosten. Die Formel hier erfasst nur den Effekt der unterjährigen Verzinsung.",[560,839,841],{"id":840},"beispiele","Beispiele",[565,843,844,845,886,887,1041,1042,1093],{},"Ein Konto bringt nominal ",[574,846,848,867],{"className":847},[577],[574,849,851],{"className":850},[581],[583,852,853],{"xmlns":585},[587,854,855,864],{},[590,856,857,860,862],{},[762,858,859],{},"6",[602,861,604],{},[596,863,608],{"mathvariant":607},[610,865,866],{"encoding":612},"6\\,\\%",[574,868,870],{"className":869,"ariaHidden":618},[617],[574,871,873,877,880,883],{"className":872},[622],[574,874],{"className":875,"style":876},[626],"height:0.8056em;vertical-align:-0.0556em;",[574,878,859],{"className":879},[631],[574,881],{"className":882,"style":724},[723],[574,884,608],{"className":885},[631],", die Zinsen werden monatlich gutgeschrieben. Pro Monat gibt es ",[574,888,890,922],{"className":889},[577],[574,891,893],{"className":892},[581],[583,894,895],{"xmlns":585},[587,896,897,919],{},[590,898,899,914,916],{},[593,900,901,903],{},[762,902,859],{},[590,904,905,908,911],{},[762,906,907],{},"100",[758,909,910],{},"⋅",[762,912,913],{},"12",[758,915,760],{},[762,917,918],{},"0,005",[610,920,921],{"encoding":612},"\\frac{6}{100 \\cdot 12} = 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",[574,1043,1045,1064],{"className":1044},[577],[574,1046,1048],{"className":1047},[581],[583,1049,1050],{"xmlns":585},[587,1051,1052,1061],{},[590,1053,1054,1057,1059],{},[762,1055,1056],{},"0,5",[602,1058,604],{},[596,1060,608],{"mathvariant":607},[610,1062,1063],{"encoding":612},"0{,}5\\,\\%",[574,1065,1067],{"className":1066,"ariaHidden":618},[617],[574,1068,1070,1074,1077,1083,1087,1090],{"className":1069},[622],[574,1071],{"className":1072,"style":1073},[626],"height:0.9444em;vertical-align:-0.1944em;",[574,1075,1028],{"className":1076},[631],[574,1078,1080],{"className":1079},[631],[574,1081,1036],{"className":1082},[1035],[574,1084,1086],{"className":1085},[631],"5",[574,1088],{"className":1089,"style":724},[723],[574,1091,608],{"className":1092},[631],":",[574,1095,1098],{"className":1096},[1097],"katex-display",[574,1099,1101,1155],{"className":1100},[577],[574,1102,1104],{"className":1103},[581],[583,1105,1107],{"xmlns":585,"display":1106},"block",[587,1108,1109,1152],{},[590,1110,1111,1119,1121,1142,1144,1146,1149],{},[1112,1113,1114,1116],"msub",{},[596,1115,565],{},[602,1117,1118],{},"eff",[758,1120,760],{},[590,1122,1123,1126,1134,1137,1139],{},[758,1124,1125],{"fence":618},"(",[1127,1128,1129,1132],"msup",{},[762,1130,1131],{},"1,005",[762,1133,913],{},[758,1135,1136],{},"−",[762,1138,764],{},[758,1140,1141],{"fence":618},")",[758,1143,910],{},[762,1145,907],{},[758,1147,1148],{},"≈",[762,1150,1151],{},"6,17",[610,1153,1154],{"encoding":612},"p_{\\text{eff}} = \\left(1{,}005^{12} - 1\\right) \\cdot 100 \\approx 6{,}17",[574,1156,1158,1226,1322,1340],{"className":1157,"ariaHidden":618},[617],[574,1159,1161,1165,1217,1220,1223],{"className":1160},[622],[574,1162],{"className":1163,"style":1164},[626],"height:0.625em;vertical-align:-0.1944em;",[574,1166,1168,1171],{"className":1167},[631],[574,1169,565],{"className":1170},[631,675],[574,1172,1175],{"className":1173},[1174],"msupsub",[574,1176,1178,1208],{"className":1177},[643,644],[574,1179,1181,1205],{"className":1180},[648],[574,1182,1185],{"className":1183,"style":1184},[652],"height:0.3361em;",[574,1186,1188,1192],{"style":1187},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[574,1189],{"className":1190,"style":1191},[660],"height:2.7em;",[574,1193,1195],{"className":1194},[665,666,667,668],[574,1196,1198],{"className":1197},[631,668],[574,1199,1202],{"className":1200},[631,1201,668],"text",[574,1203,1118],{"className":1204},[631,668],[574,1206,706],{"className":1207},[705],[574,1209,1211],{"className":1210},[648],[574,1212,1215],{"className":1213,"style":1214},[652],"height:0.15em;",[574,1216],{},[574,1218],{"className":1219,"style":784},[723],[574,1221,760],{"className":1222},[788],[574,1224],{"className":1225,"style":784},[723],[574,1227,1229,1233,1313,1316,1319],{"className":1228},[622],[574,1230],{"className":1231,"style":1232},[626],"height:1.2141em;vertical-align:-0.35em;",[574,1234,1237,1247,1250,1256,1260,1294,1298,1301,1304,1307],{"className":1235},[1236],"minner",[574,1238,1242],{"className":1239,"style":1241},[635,1240],"delimcenter","top:0em;",[574,1243,1125],{"className":1244},[1245,1246],"delimsizing","size1",[574,1248,764],{"className":1249},[631],[574,1251,1253],{"className":1252},[631],[574,1254,1036],{"className":1255},[1035],[574,1257,1259],{"className":1258},[631],"00",[574,1261,1263,1266],{"className":1262},[631],[574,1264,1086],{"className":1265},[631],[574,1267,1269],{"className":1268},[1174],[574,1270,1272],{"className":1271},[643],[574,1273,1275],{"className":1274},[648],[574,1276,1279],{"className":1277,"style":1278},[652],"height:0.8641em;",[574,1280,1282,1285],{"style":1281},"top:-3.113em;margin-right:0.05em;",[574,1283],{"className":1284,"style":1191},[660],[574,1286,1288],{"className":1287},[665,666,667,668],[574,1289,1291],{"className":1290},[631,668],[574,1292,913],{"className":1293},[631,668],[574,1295],{"className":1296,"style":1297},[723],"margin-right:0.2222em;",[574,1299,1136],{"className":1300},[968],[574,1302],{"className":1303,"style":1297},[723],[574,1305,764],{"className":1306},[631],[574,1308,1310],{"className":1309,"style":1241},[719,1240],[574,1311,1141],{"className":1312},[1245,1246],[574,1314],{"className":1315,"style":1297},[723],[574,1317,910],{"className":1318},[968],[574,1320],{"className":1321,"style":1297},[723],[574,1323,1325,1328,1331,1334,1337],{"className":1324},[622],[574,1326],{"className":1327,"style":798},[626],[574,1329,907],{"className":1330},[631],[574,1332],{"className":1333,"style":784},[723],[574,1335,1148],{"className":1336},[788],[574,1338],{"className":1339,"style":784},[723],[574,1341,1343,1346,1349,1355],{"className":1342},[622],[574,1344],{"className":1345,"style":1024},[626],[574,1347,859],{"className":1348},[631],[574,1350,1352],{"className":1351},[631],[574,1353,1036],{"className":1354},[1035],[574,1356,1358],{"className":1357},[631],"17",[565,1360,1361,1362,1410],{},"Der effektive Jahreszins beträgt rund ",[574,1363,1365,1383],{"className":1364},[577],[574,1366,1368],{"className":1367},[581],[583,1369,1370],{"xmlns":585},[587,1371,1372,1380],{},[590,1373,1374,1376,1378],{},[762,1375,1151],{},[602,1377,604],{},[596,1379,608],{"mathvariant":607},[610,1381,1382],{"encoding":612},"6{,}17\\,\\%",[574,1384,1386],{"className":1385,"ariaHidden":618},[617],[574,1387,1389,1392,1395,1401,1404,1407],{"className":1388},[622],[574,1390],{"className":1391,"style":1073},[626],[574,1393,859],{"className":1394},[631],[574,1396,1398],{"className":1397},[631],[574,1399,1036],{"className":1400},[1035],[574,1402,1358],{"className":1403},[631],[574,1405],{"className":1406,"style":724},[723],[574,1408,608],{"className":1409},[631],".",[565,1412,1413,1414,1454,1455,1494,1495,1728,1729,1758,1759,1887,1888,1973],{},"Nominal ",[574,1415,1417,1436],{"className":1416},[577],[574,1418,1420],{"className":1419},[581],[583,1421,1422],{"xmlns":585},[587,1423,1424,1433],{},[590,1425,1426,1429,1431],{},[762,1427,1428],{},"4",[602,1430,604],{},[596,1432,608],{"mathvariant":607},[610,1434,1435],{"encoding":612},"4\\,\\%",[574,1437,1439],{"className":1438,"ariaHidden":618},[617],[574,1440,1442,1445,1448,1451],{"className":1441},[622],[574,1443],{"className":1444,"style":876},[626],[574,1446,1428],{"className":1447},[631],[574,1449],{"className":1450,"style":724},[723],[574,1452,608],{"className":1453},[631]," mit vierteljährlicher Gutschrift (",[574,1456,1458,1476],{"className":1457},[577],[574,1459,1461],{"className":1460},[581],[583,1462,1463],{"xmlns":585},[587,1464,1465,1473],{},[590,1466,1467,1469,1471],{},[762,1468,764],{},[602,1470,604],{},[596,1472,608],{"mathvariant":607},[610,1474,1475],{"encoding":612},"1\\,\\%",[574,1477,1479],{"className":1478,"ariaHidden":618},[617],[574,1480,1482,1485,1488,1491],{"className":1481},[622],[574,1483],{"className":1484,"style":876},[626],[574,1486,764],{"className":1487},[631],[574,1489],{"className":1490,"style":724},[723],[574,1492,608],{"className":1493},[631]," pro Quartal): ",[574,1496,1498,1543],{"className":1497},[577],[574,1499,1501],{"className":1500},[581],[583,1502,1503],{"xmlns":585},[587,1504,1505,1540],{},[590,1506,1507,1513,1515,1518,1525,1527,1529,1531,1533,1535,1537],{},[1112,1508,1509,1511],{},[596,1510,565],{},[602,1512,1118],{},[758,1514,760],{},[758,1516,1125],{"stretchy":1517},"false",[1127,1519,1520,1523],{},[762,1521,1522],{},"1,01",[762,1524,1428],{},[758,1526,1136],{},[762,1528,764],{},[758,1530,1141],{"stretchy":1517},[758,1532,910],{},[762,1534,907],{},[758,1536,1148],{},[762,1538,1539],{},"4,06",[610,1541,1542],{"encoding":612},"p_{\\text{eff}} = (1{,}01^4 - 1) \\cdot 100 \\approx 4{,}06",[574,1544,1546,1607,1669,1691,1709],{"className":1545,"ariaHidden":618},[617],[574,1547,1549,1552,1598,1601,1604],{"className":1548},[622],[574,1550],{"className":1551,"style":1164},[626],[574,1553,1555,1558],{"className":1554},[631],[574,1556,565],{"className":1557},[631,675],[574,1559,1561],{"className":1560},[1174],[574,1562,1564,1590],{"className":1563},[643,644],[574,1565,1567,1587],{"className":1566},[648],[574,1568,1570],{"className":1569,"style":1184},[652],[574,1571,1572,1575],{"style":1187},[574,1573],{"className":1574,"style":1191},[660],[574,1576,1578],{"className":1577},[665,666,667,668],[574,1579,1581],{"className":1580},[631,668],[574,1582,1584],{"className":1583},[631,1201,668],[574,1585,1118],{"className":1586},[631,668],[574,1588,706],{"className":1589},[705],[574,1591,1593],{"className":1592},[648],[574,1594,1596],{"className":1595,"style":1214},[652],[574,1597],{},[574,1599],{"className":1600,"style":784},[723],[574,1602,760],{"className":1603},[788],[574,1605],{"className":1606,"style":784},[723],[574,1608,1610,1614,1617,1620,1626,1629,1660,1663,1666],{"className":1609},[622],[574,1611],{"className":1612,"style":1613},[626],"height:1.0641em;vertical-align:-0.25em;",[574,1615,1125],{"className":1616},[635],[574,1618,764],{"className":1619},[631],[574,1621,1623],{"className":1622},[631],[574,1624,1036],{"className":1625},[1035],[574,1627,1028],{"className":1628},[631],[574,1630,1632,1635],{"className":1631},[631],[574,1633,764],{"className":1634},[631],[574,1636,1638],{"className":1637},[1174],[574,1639,1641],{"className":1640},[643],[574,1642,1644],{"className":1643},[648],[574,1645,1648],{"className":1646,"style":1647},[652],"height:0.8141em;",[574,1649,1651,1654],{"style":1650},"top:-3.063em;margin-right:0.05em;",[574,1652],{"className":1653,"style":1191},[660],[574,1655,1657],{"className":1656},[665,666,667,668],[574,1658,1428],{"className":1659},[631,668],[574,1661],{"className":1662,"style":1297},[723],[574,1664,1136],{"className":1665},[968],[574,1667],{"className":1668,"style":1297},[723],[574,1670,1672,1676,1679,1682,1685,1688],{"className":1671},[622],[574,1673],{"className":1674,"style":1675},[626],"height:1em;vertical-align:-0.25em;",[574,1677,764],{"className":1678},[631],[574,1680,1141],{"className":1681},[719],[574,1683],{"className":1684,"style":1297},[723],[574,1686,910],{"className":1687},[968],[574,1689],{"className":1690,"style":1297},[723],[574,1692,1694,1697,1700,1703,1706],{"className":1693},[622],[574,1695],{"className":1696,"style":798},[626],[574,1698,907],{"className":1699},[631],[574,1701],{"className":1702,"style":784},[723],[574,1704,1148],{"className":1705},[788],[574,1707],{"className":1708,"style":784},[723],[574,1710,1712,1715,1718,1724],{"className":1711},[622],[574,1713],{"className":1714,"style":1024},[626],[574,1716,1428],{"className":1717},[631],[574,1719,1721],{"className":1720},[631],[574,1722,1036],{"className":1723},[1035],[574,1725,1727],{"className":1726},[631],"06",". Aus ",[574,1730,1732,1746],{"className":1731},[577],[574,1733,1735],{"className":1734},[581],[583,1736,1737],{"xmlns":585},[587,1738,1739,1744],{},[590,1740,1741],{},[762,1742,1743],{},"5000",[610,1745,1743],{"encoding":612},[574,1747,1749],{"className":1748,"ariaHidden":618},[617],[574,1750,1752,1755],{"className":1751},[622],[574,1753],{"className":1754,"style":798},[626],[574,1756,1743],{"className":1757},[631]," € werden in einem Jahr ",[574,1760,1762,1789],{"className":1761},[577],[574,1763,1765],{"className":1764},[581],[583,1766,1767],{"xmlns":585},[587,1768,1769,1786],{},[590,1770,1771,1773,1775,1781,1783],{},[762,1772,1743],{},[758,1774,910],{},[1127,1776,1777,1779],{},[762,1778,1522],{},[762,1780,1428],{},[758,1782,1148],{},[762,1784,1785],{},"5203,02",[610,1787,1788],{"encoding":612},"5000 \\cdot 1{,}01^4 \\approx 5203{,}02",[574,1790,1792,1810,1867],{"className":1791,"ariaHidden":618},[617],[574,1793,1795,1798,1801,1804,1807],{"className":1794},[622],[574,1796],{"className":1797,"style":798},[626],[574,1799,1743],{"className":1800},[631],[574,1802],{"className":1803,"style":1297},[723],[574,1805,910],{"className":1806},[968],[574,1808],{"className":1809,"style":1297},[723],[574,1811,1813,1817,1820,1826,1829,1858,1861,1864],{"className":1812},[622],[574,1814],{"className":1815,"style":1816},[626],"height:1.0085em;vertical-align:-0.1944em;",[574,1818,764],{"className":1819},[631],[574,1821,1823],{"className":1822},[631],[574,1824,1036],{"className":1825},[1035],[574,1827,1028],{"className":1828},[631],[574,1830,1832,1835],{"className":1831},[631],[574,1833,764],{"className":1834},[631],[574,1836,1838],{"className":1837},[1174],[574,1839,1841],{"className":1840},[643],[574,1842,1844],{"className":1843},[648],[574,1845,1847],{"className":1846,"style":1647},[652],[574,1848,1849,1852],{"style":1650},[574,1850],{"className":1851,"style":1191},[660],[574,1853,1855],{"className":1854},[665,666,667,668],[574,1856,1428],{"className":1857},[631,668],[574,1859],{"className":1860,"style":784},[723],[574,1862,1148],{"className":1863},[788],[574,1865],{"className":1866,"style":784},[723],[574,1868,1870,1873,1877,1883],{"className":1869},[622],[574,1871],{"className":1872,"style":1024},[626],[574,1874,1876],{"className":1875},[631],"5203",[574,1878,1880],{"className":1879},[631],[574,1881,1036],{"className":1882},[1035],[574,1884,1886],{"className":1885},[631],"02"," € statt ",[574,1889,1891,1915],{"className":1890},[577],[574,1892,1894],{"className":1893},[581],[583,1895,1896],{"xmlns":585},[587,1897,1898,1912],{},[590,1899,1900,1902,1904,1907,1909],{},[762,1901,1743],{},[758,1903,910],{},[762,1905,1906],{},"1,04",[758,1908,760],{},[762,1910,1911],{},"5200",[610,1913,1914],{"encoding":612},"5000 \\cdot 1{,}04 = 5200",[574,1916,1918,1936,1964],{"className":1917,"ariaHidden":618},[617],[574,1919,1921,1924,1927,1930,1933],{"className":1920},[622],[574,1922],{"className":1923,"style":798},[626],[574,1925,1743],{"className":1926},[631],[574,1928],{"className":1929,"style":1297},[723],[574,1931,910],{"className":1932},[968],[574,1934],{"className":1935,"style":1297},[723],[574,1937,1939,1942,1945,1951,1955,1958,1961],{"className":1938},[622],[574,1940],{"className":1941,"style":1024},[626],[574,1943,764],{"className":1944},[631],[574,1946,1948],{"className":1947},[631],[574,1949,1036],{"className":1950},[1035],[574,1952,1954],{"className":1953},[631],"04",[574,1956],{"className":1957,"style":784},[723],[574,1959,760],{"className":1960},[788],[574,1962],{"className":1963,"style":784},[723],[574,1965,1967,1970],{"className":1966},[622],[574,1968],{"className":1969,"style":798},[626],[574,1971,1911],{"className":1972},[631]," €.",[565,1975,1976,1977,2016,2017,2223,2224,1410],{},"Umgekehrt: Welcher Nominalzins mit monatlicher Gutschrift ergibt effektiv ",[574,1978,1980,1998],{"className":1979},[577],[574,1981,1983],{"className":1982},[581],[583,1984,1985],{"xmlns":585},[587,1986,1987,1995],{},[590,1988,1989,1991,1993],{},[762,1990,1086],{},[602,1992,604],{},[596,1994,608],{"mathvariant":607},[610,1996,1997],{"encoding":612},"5\\,\\%",[574,1999,2001],{"className":2000,"ariaHidden":618},[617],[574,2002,2004,2007,2010,2013],{"className":2003},[622],[574,2005],{"className":2006,"style":876},[626],[574,2008,1086],{"className":2009},[631],[574,2011],{"className":2012,"style":724},[723],[574,2014,608],{"className":2015},[631],"? Aus ",[574,2018,2020,2059],{"className":2019},[577],[574,2021,2023],{"className":2022},[581],[583,2024,2025],{"xmlns":585},[587,2026,2027,2056],{},[590,2028,2029,2051,2053],{},[1127,2030,2031,2049],{},[590,2032,2033,2035,2037,2040,2047],{},[758,2034,1125],{"fence":618},[762,2036,764],{},[758,2038,2039],{},"+",[593,2041,2042,2044],{},[596,2043,565],{},[762,2045,2046],{},"1200",[758,2048,1141],{"fence":618},[762,2050,913],{},[758,2052,760],{},[762,2054,2055],{},"1,05",[610,2057,2058],{"encoding":612},"\\left(1 + \\frac{p}{1200}\\right)^{12} = 1{,}05",[574,2060,2062,2204],{"className":2061,"ariaHidden":618},[617],[574,2063,2065,2069,2195,2198,2201],{"className":2064},[622],[574,2066],{"className":2067,"style":2068},[626],"height:1.404em;vertical-align:-0.35em;",[574,2070,2072,2167],{"className":2071},[1236],[574,2073,2075,2081,2084,2087,2090,2093,2161],{"className":2074},[1236],[574,2076,2078],{"className":2077,"style":1241},[635,1240],[574,2079,1125],{"className":2080},[1245,1246],[574,2082,764],{"className":2083},[631],[574,2085],{"className":2086,"style":1297},[723],[574,2088,2039],{"className":2089},[968],[574,2091],{"className":2092,"style":1297},[723],[574,2094,2096,2099,2158],{"className":2095},[631],[574,2097],{"className":2098},[635,636],[574,2100,2102],{"className":2101},[593],[574,2103,2105,2150],{"className":2104},[643,644],[574,2106,2108,2147],{"className":2107},[648],[574,2109,2111,2125,2133],{"className":2110,"style":653},[652],[574,2112,2113,2116],{"style":656},[574,2114],{"className":2115,"style":661},[660],[574,2117,2119],{"className":2118},[665,666,667,668],[574,2120,2122],{"className":2121},[631,668],[574,2123,2046],{"className":2124},[631,668],[574,2126,2127,2130],{"style":678},[574,2128],{"className":2129,"style":661},[660],[574,2131],{"className":2132,"style":686},[685],[574,2134,2135,2138],{"style":689},[574,2136],{"className":2137,"style":661},[660],[574,2139,2141],{"className":2140},[665,666,667,668],[574,2142,2144],{"className":2143},[631,668],[574,2145,565],{"className":2146},[631,675,668],[574,2148,706],{"className":2149},[705],[574,2151,2153],{"className":2152},[648],[574,2154,2156],{"className":2155,"style":713},[652],[574,2157],{},[574,2159],{"className":2160},[719,636],[574,2162,2164],{"className":2163,"style":1241},[719,1240],[574,2165,1141],{"className":2166},[1245,1246],[574,2168,2170],{"className":2169},[1174],[574,2171,2173],{"className":2172},[643],[574,2174,2176],{"className":2175},[648],[574,2177,2180],{"className":2178,"style":2179},[652],"height:1.054em;",[574,2181,2183,2186],{"style":2182},"top:-3.3029em;margin-right:0.05em;",[574,2184],{"className":2185,"style":1191},[660],[574,2187,2189],{"className":2188},[665,666,667,668],[574,2190,2192],{"className":2191},[631,668],[574,2193,913],{"className":2194},[631,668],[574,2196],{"className":2197,"style":784},[723],[574,2199,760],{"className":2200},[788],[574,2202],{"className":2203,"style":784},[723],[574,2205,2207,2210,2213,2219],{"className":2206},[622],[574,2208],{"className":2209,"style":1024},[626],[574,2211,764],{"className":2212},[631],[574,2214,2216],{"className":2215},[631],[574,2217,1036],{"className":2218},[1035],[574,2220,2222],{"className":2221},[631],"05"," folgt ",[574,2225,2227,2269],{"className":2226},[577],[574,2228,2230],{"className":2229},[581],[583,2231,2232],{"xmlns":585},[587,2233,2234,2266],{},[590,2235,2236,2238,2240,2242,2244,2261,2263],{},[596,2237,565],{},[758,2239,760],{},[762,2241,2046],{},[758,2243,910],{},[590,2245,2246,2248,2255,2257,2259],{},[758,2247,1125],{"fence":618},[2249,2250,2251,2253],"mroot",{},[762,2252,2055],{},[762,2254,913],{},[758,2256,1136],{},[762,2258,764],{},[758,2260,1141],{"fence":618},[758,2262,1148],{},[762,2264,2265],{},"4,89",[610,2267,2268],{"encoding":612},"p = 1200 \\cdot \\left(\\sqrt[12]{1{,}05} - 1\\right) \\approx 4{,}89",[574,2270,2272,2290,2308,2454],{"className":2271,"ariaHidden":618},[617],[574,2273,2275,2278,2281,2284,2287],{"className":2274},[622],[574,2276],{"className":2277,"style":1164},[626],[574,2279,565],{"className":2280},[631,675],[574,2282],{"className":2283,"style":784},[723],[574,2285,760],{"className":2286},[788],[574,2288],{"className":2289,"style":784},[723],[574,2291,2293,2296,2299,2302,2305],{"className":2292},[622],[574,2294],{"className":2295,"style":798},[626],[574,2297,2046],{"className":2298},[631],[574,2300],{"className":2301,"style":1297},[723],[574,2303,910],{"className":2304},[968],[574,2306],{"className":2307,"style":1297},[723],[574,2309,2311,2315,2445,2448,2451],{"className":2310},[622],[574,2312],{"className":2313,"style":2314},[626],"height:1.2em;vertical-align:-0.35em;",[574,2316,2318,2324,2427,2430,2433,2436,2439],{"className":2317},[1236],[574,2319,2321],{"className":2320,"style":1241},[635,1240],[574,2322,1125],{"className":2323},[1245,1246],[574,2325,2328,2358],{"className":2326},[631,2327],"sqrt",[574,2329,2332],{"className":2330},[2331],"root",[574,2333,2335],{"className":2334},[643],[574,2336,2338],{"className":2337},[648],[574,2339,2342],{"className":2340,"style":2341},[652],"height:0.6702em;",[574,2343,2345,2349],{"style":2344},"top:-2.848em;",[574,2346],{"className":2347,"style":2348},[660],"height:2.5em;",[574,2350,2352],{"className":2351},[665,666,1246,668],[574,2353,2355],{"className":2354},[631,668],[574,2356,913],{"className":2357},[631,668],[574,2359,2361,2418],{"className":2360},[643,644],[574,2362,2364,2415],{"className":2363},[648],[574,2365,2368,2392],{"className":2366,"style":2367},[652],"height:0.81em;",[574,2369,2373,2376],{"className":2370,"style":2372},[2371],"svg-align","top:-3em;",[574,2374],{"className":2375,"style":661},[660],[574,2377,2380,2383,2389],{"className":2378,"style":2379},[631],"padding-left:0.833em;",[574,2381,764],{"className":2382},[631],[574,2384,2386],{"className":2385},[631],[574,2387,1036],{"className":2388},[1035],[574,2390,2222],{"className":2391},[631],[574,2393,2395,2398],{"style":2394},"top:-2.77em;",[574,2396],{"className":2397,"style":661},[660],[574,2399,2403],{"className":2400,"style":2402},[2401],"hide-tail","min-width:0.853em;height:1.08em;",[2404,2405,2411],"svg",{"xmlns":2406,"width":2407,"height":2408,"viewBox":2409,"preserveAspectRatio":2410},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[2412,2413],"path",{"d":2414},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[574,2416,706],{"className":2417},[705],[574,2419,2421],{"className":2420},[648],[574,2422,2425],{"className":2423,"style":2424},[652],"height:0.23em;",[574,2426],{},[574,2428],{"className":2429,"style":1297},[723],[574,2431,1136],{"className":2432},[968],[574,2434],{"className":2435,"style":1297},[723],[574,2437,764],{"className":2438},[631],[574,2440,2442],{"className":2441,"style":1241},[719,1240],[574,2443,1141],{"className":2444},[1245,1246],[574,2446],{"className":2447,"style":784},[723],[574,2449,1148],{"className":2450},[788],[574,2452],{"className":2453,"style":784},[723],[574,2455,2457,2460,2463,2469],{"className":2456},[622],[574,2458],{"className":2459,"style":1024},[626],[574,2461,1428],{"className":2462},[631],[574,2464,2466],{"className":2465},[631],[574,2467,1036],{"className":2468},[1035],[574,2470,2472],{"className":2471},[631],"89",[560,2474,2476],{"id":2475},"typische-fehler","Typische Fehler",[737,2478,2479,2587,2590],{},[740,2480,2481,2482,2510,2511,2586],{},"Den Jahreszins nicht durch ",[574,2483,2485,2498],{"className":2484},[577],[574,2486,2488],{"className":2487},[581],[583,2489,2490],{"xmlns":585},[587,2491,2492,2496],{},[590,2493,2494],{},[596,2495,600],{},[610,2497,600],{"encoding":612},[574,2499,2501],{"className":2500,"ariaHidden":618},[617],[574,2502,2504,2507],{"className":2503},[622],[574,2505],{"className":2506,"style":777},[626],[574,2508,600],{"className":2509},[631,675]," teilen, also ",[574,2512,2514,2533],{"className":2513},[577],[574,2515,2517],{"className":2516},[581],[583,2518,2519],{"xmlns":585},[587,2520,2521,2530],{},[590,2522,2523],{},[1127,2524,2525,2528],{},[762,2526,2527],{},"1,06",[762,2529,913],{},[610,2531,2532],{"encoding":612},"1{,}06^{12}",[574,2534,2536],{"className":2535,"ariaHidden":618},[617],[574,2537,2539,2542,2545,2551,2554],{"className":2538},[622],[574,2540],{"className":2541,"style":1816},[626],[574,2543,764],{"className":2544},[631],[574,2546,2548],{"className":2547},[631],[574,2549,1036],{"className":2550},[1035],[574,2552,1028],{"className":2553},[631],[574,2555,2557,2560],{"className":2556},[631],[574,2558,859],{"className":2559},[631],[574,2561,2563],{"className":2562},[1174],[574,2564,2566],{"className":2565},[643],[574,2567,2569],{"className":2568},[648],[574,2570,2572],{"className":2571,"style":1647},[652],[574,2573,2574,2577],{"style":1650},[574,2575],{"className":2576,"style":1191},[660],[574,2578,2580],{"className":2579},[665,666,667,668],[574,2581,2583],{"className":2582},[631,668],[574,2584,913],{"className":2585},[631,668]," rechnen. Pro Monat gibt es nur ein Zwölftel des Jahreszinses.",[740,2588,2589],{},"Den Effektivzins für kleiner als den Nominalzins halten. Bei positiven Zinsen ist er immer mindestens so groß.",[740,2591,2592,2593,2621],{},"Den Monatszins einfach mal ",[574,2594,2596,2609],{"className":2595},[577],[574,2597,2599],{"className":2598},[581],[583,2600,2601],{"xmlns":585},[587,2602,2603,2607],{},[590,2604,2605],{},[762,2606,913],{},[610,2608,913],{"encoding":612},[574,2610,2612],{"className":2611,"ariaHidden":618},[617],[574,2613,2615,2618],{"className":2614},[622],[574,2616],{"className":2617,"style":798},[626],[574,2619,913],{"className":2620},[631]," nehmen und das für den Effektivzins halten. So erhält man den Nominalzins, nicht den Effektivzins.",{"title":2623,"searchDepth":2624,"depth":2624,"links":2625},"",2,[2626,2627,2628],{"id":562,"depth":2624,"text":563},{"id":840,"depth":2624,"text":841},{"id":2475,"depth":2624,"text":2476},[2630,2632,2635,2638,2641,2644,2646],{"lhs":2631,"rhs":565},"((1 + p\u002F100)^1 - 1)*100",{"lhs":2633,"rhs":2634},"6 \u002F (100 * 12)","0.005",{"lhs":2636,"rhs":2637},"round((1.005^12 - 1)*100, 2)","6.17",{"lhs":2639,"rhs":2640},"round((1.01^4 - 1)*100, 2)","4.06",{"lhs":2642,"rhs":2643},"round(5000 * 1.01^4, 2)","5203.02",{"lhs":2645,"rhs":1911},"5000 * 1.04",{"lhs":2647,"rhs":2648},"round((1.05^(1\u002F12) - 1)*100*12, 2)","4.89","m \\in \\mathbb{N},\\ m \\geq 1,\\ p > -100 m","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>m\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">N\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">m \\in \\mathbb{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:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">m\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:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">N\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>m\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">m \\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\">m\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\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>100\u003C\u002Fmn>\u003Cmi>m\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p > -100 m\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:0.7278em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">−\u003C\u002Fspan>\u003Cspan class=\"mord\">100\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">m\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","effective-interest-rate","p_{\\text{eff}} = \\left( \\left(1 + \\frac{p}{100 \\cdot m}\\right)^m - 1 \\right) \\cdot 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>p\u003C\u002Fmi>\u003Cmtext>eff\u003C\u002Fmtext>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmsup>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>+\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>p\u003C\u002Fmi>\u003Cmrow>\u003Cmn>100\u003C\u002Fmn>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>m\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmi>m\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmn>100\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p_{\\text{eff}} = \\left( \\left(1 + \\frac{p}{100 \\cdot m}\\right)^m - 1 \\right) \\cdot 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:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3361em;\">\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\">eff\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 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