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e^{rt}",[569,1054,1056,1085],{"className":1055,"ariaHidden":599},[598],[569,1057,1059,1063,1067,1070,1073,1076,1079,1082],{"className":1058},[603],[569,1060],{"className":1061,"style":1062},[607],"height:1em;vertical-align:-0.25em;",[569,1064,1021],{"className":1065,"style":1066},[612,613],"margin-right:0.0715em;",[569,1068,699],{"className":1069},[830],[569,1071,1027],{"className":1072},[612,613],[569,1074,717],{"className":1075},[923],[569,1077],{"className":1078,"style":960},[818],[569,1080,722],{"className":1081},[786],[569,1083],{"className":1084,"style":960},[818],[569,1086,1088,1092,1135],{"className":1087},[603],[569,1089],{"className":1090,"style":1091},[607],"height:0.9436em;vertical-align:-0.15em;",[569,1093,1095,1098],{"className":1094},[612],[569,1096,1021],{"className":1097,"style":1066},[612,613],[569,1099,1101],{"className":1100},[933],[569,1102,1104,1126],{"className":1103},[751,752],[569,1105,1107,1123],{"className":1106},[756],[569,1108,1111],{"className":1109,"style":1110},[760],"height:0.3011em;",[569,1112,1114,1117],{"style":1113},"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;",[569,1115],{"className":1116,"style":950},[768],[569,1118,1120],{"className":1119},[773,774,775,776],[569,1121,1039],{"className":1122},[612,776],[569,1124,805],{"className":1125},[804],[569,1127,1129],{"className":1128},[756],[569,1130,1133],{"className":1131,"style":1132},[760],"height:0.15em;",[569,1134],{},[569,1136,1138,1141],{"className":1137},[612],[569,1139,727],{"className":1140},[612,613],[569,1142,1144],{"className":1143},[933],[569,1145,1147],{"className":1146},[751],[569,1148,1150],{"className":1149},[756],[569,1151,1154],{"className":1152,"style":1153},[760],"height:0.7936em;",[569,1155,1157,1160],{"style":1156},"top:-3.063em;margin-right:0.05em;",[569,1158],{"className":1159,"style":950},[768],[569,1161,1163],{"className":1162},[773,774,775,776],[569,1164,1166,1169],{"className":1165},[612,776],[569,1167,712],{"className":1168,"style":907},[612,613,776],[569,1170,1027],{"className":1171},[612,613,776],". Es erfüllt die Differentialgleichung ",[569,1174,1176,1217],{"className":1175},[572],[569,1177,1179],{"className":1178},[576],[578,1180,1181],{"xmlns":580},[582,1182,1183,1214],{},[585,1184,1185,1193,1195,1197,1199,1201,1203,1206,1208,1210,1212],{},[693,1186,1187,1189],{},[588,1188,1021],{},[678,1190,1192],{"mathvariant":690,"lspace":1191,"rspace":1191},"0em","′",[678,1194,699],{"stretchy":1024},[588,1196,1027],{},[678,1198,717],{"stretchy":1024},[678,1200,722],{},[588,1202,712],{},[678,1204,1205],{},"⋅",[588,1207,1021],{},[678,1209,699],{"stretchy":1024},[588,1211,1027],{},[678,1213,717],{"stretchy":1024},[592,1215,1216],{"encoding":594},"K'(t) = r \\cdot K(t)",[569,1218,1220,1278,1297],{"className":1219,"ariaHidden":599},[598],[569,1221,1223,1227,1260,1263,1266,1269,1272,1275],{"className":1222},[603],[569,1224],{"className":1225,"style":1226},[607],"height:1.0019em;vertical-align:-0.25em;",[569,1228,1230,1233],{"className":1229},[612],[569,1231,1021],{"className":1232,"style":1066},[612,613],[569,1234,1236],{"className":1235},[933],[569,1237,1239],{"className":1238},[751],[569,1240,1242],{"className":1241},[756],[569,1243,1246],{"className":1244,"style":1245},[760],"height:0.7519em;",[569,1247,1248,1251],{"style":1156},[569,1249],{"className":1250,"style":950},[768],[569,1252,1254],{"className":1253},[773,774,775,776],[569,1255,1257],{"className":1256},[612,776],[569,1258,1192],{"className":1259},[612,776],[569,1261,699],{"className":1262},[830],[569,1264,1027],{"className":1265},[612,613],[569,1267,717],{"className":1268},[923],[569,1270],{"className":1271,"style":960},[818],[569,1273,722],{"className":1274},[786],[569,1276],{"className":1277,"style":960},[818],[569,1279,1281,1285,1288,1291,1294],{"className":1280},[603],[569,1282],{"className":1283,"style":1284},[607],"height:0.4445em;",[569,1286,712],{"className":1287,"style":907},[612,613],[569,1289],{"className":1290,"style":844},[818],[569,1292,1205],{"className":1293},[848],[569,1295],{"className":1296,"style":844},[818],[569,1298,1300,1303,1306,1309,1312],{"className":1299},[603],[569,1301],{"className":1302,"style":1062},[607],[569,1304,1021],{"className":1305,"style":1066},[612,613],[569,1307,699],{"className":1308},[830],[569,1310,1027],{"className":1311},[612,613],[569,1313,717],{"className":1314},[923],": Die momentane Wachstumsrate ist proportional zum aktuellen Kapital.",[565,1317,1318],{},"Wichtige Zusammenhänge:",[1320,1321,1322,1519,1725],"ul",{},[1323,1324,1325,1326,1518],"li",{},"Effektiver Jahreszins: ",[569,1327,1329,1371],{"className":1328},[572],[569,1330,1332],{"className":1331},[576],[578,1333,1334],{"xmlns":580},[582,1335,1336,1368],{},[585,1337,1338,1346,1348,1350,1356,1359,1361,1363,1365],{},[1033,1339,1340,1342],{},[588,1341,565],{},[1343,1344,1345],"mtext",{},"eff",[678,1347,722],{},[678,1349,699],{"stretchy":1024},[693,1351,1352,1354],{},[588,1353,727],{},[588,1355,712],{},[678,1357,1358],{},"−",[701,1360,703],{},[678,1362,717],{"stretchy":1024},[678,1364,1205],{},[701,1366,1367],{},"100",[592,1369,1370],{"encoding":594},"p_{\\text{eff}} = (e^r - 1) \\cdot 100",[569,1372,1374,1439,1487,1508],{"className":1373,"ariaHidden":599},[598],[569,1375,1377,1381,1430,1433,1436],{"className":1376},[603],[569,1378],{"className":1379,"style":1380},[607],"height:0.625em;vertical-align:-0.1944em;",[569,1382,1384,1387],{"className":1383},[612],[569,1385,565],{"className":1386},[612,613],[569,1388,1390],{"className":1389},[933],[569,1391,1393,1422],{"className":1392},[751,752],[569,1394,1396,1419],{"className":1395},[756],[569,1397,1400],{"className":1398,"style":1399},[760],"height:0.3361em;",[569,1401,1403,1406],{"style":1402},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[569,1404],{"className":1405,"style":950},[768],[569,1407,1409],{"className":1408},[773,774,775,776],[569,1410,1412],{"className":1411},[612,776],[569,1413,1416],{"className":1414},[612,1415,776],"text",[569,1417,1345],{"className":1418},[612,776],[569,1420,805],{"className":1421},[804],[569,1423,1425],{"className":1424},[756],[569,1426,1428],{"className":1427,"style":1132},[760],[569,1429],{},[569,1431],{"className":1432,"style":960},[818],[569,1434,722],{"className":1435},[786],[569,1437],{"className":1438,"style":960},[818],[569,1440,1442,1445,1448,1478,1481,1484],{"className":1441},[603],[569,1443],{"className":1444,"style":1062},[607],[569,1446,699],{"className":1447},[830],[569,1449,1451,1454],{"className":1450},[612],[569,1452,727],{"className":1453},[612,613],[569,1455,1457],{"className":1456},[933],[569,1458,1460],{"className":1459},[751],[569,1461,1463],{"className":1462},[756],[569,1464,1467],{"className":1465,"style":1466},[760],"height:0.6644em;",[569,1468,1469,1472],{"style":1156},[569,1470],{"className":1471,"style":950},[768],[569,1473,1475],{"className":1474},[773,774,775,776],[569,1476,712],{"className":1477,"style":907},[612,613,776],[569,1479],{"className":1480,"style":844},[818],[569,1482,1358],{"className":1483},[848],[569,1485],{"className":1486,"style":844},[818],[569,1488,1490,1493,1496,1499,1502,1505],{"className":1489},[603],[569,1491],{"className":1492,"style":1062},[607],[569,1494,703],{"className":1495},[612],[569,1497,717],{"className":1498},[923],[569,1500],{"className":1501,"style":844},[818],[569,1503,1205],{"className":1504},[848],[569,1506],{"className":1507,"style":844},[818],[569,1509,1511,1515],{"className":1510},[603],[569,1512],{"className":1513,"style":1514},[607],"height:0.6444em;",[569,1516,1367],{"className":1517},[612],".",[1323,1520,1521,1522,1550,1551,1518],{},"Ein jährlicher Zinssatz ",[569,1523,1525,1538],{"className":1524},[572],[569,1526,1528],{"className":1527},[576],[578,1529,1530],{"xmlns":580},[582,1531,1532,1536],{},[585,1533,1534],{},[588,1535,565],{},[592,1537,565],{"encoding":594},[569,1539,1541],{"className":1540,"ariaHidden":599},[598],[569,1542,1544,1547],{"className":1543},[603],[569,1545],{"className":1546,"style":1380},[607],[569,1548,565],{"className":1549},[612,613]," entspricht dem stetigen Zinssatz ",[569,1552,1554,1591],{"className":1553},[572],[569,1555,1557],{"className":1556},[576],[578,1558,1559],{"xmlns":580},[582,1560,1561,1588],{},[585,1562,1563,1565,1567,1570,1572],{},[588,1564,712],{},[678,1566,722],{},[588,1568,1569],{},"ln",[678,1571,680],{},[585,1573,1574,1576,1578,1580,1586],{},[678,1575,699],{"fence":599},[701,1577,703],{},[678,1579,706],{},[708,1581,1582,1584],{},[588,1583,565],{},[701,1585,1367],{},[678,1587,717],{"fence":599},[592,1589,1590],{"encoding":594},"r = \\ln\\left(1 + \\frac{p}{100}\\right)",[569,1592,1594,1612],{"className":1593,"ariaHidden":599},[598],[569,1595,1597,1600,1603,1606,1609],{"className":1596},[603],[569,1598],{"className":1599,"style":608},[607],[569,1601,712],{"className":1602,"style":907},[612,613],[569,1604],{"className":1605,"style":960},[818],[569,1607,722],{"className":1608},[786],[569,1610],{"className":1611,"style":960},[818],[569,1613,1615,1619,1622,1625],{"className":1614},[603],[569,1616],{"className":1617,"style":1618},[607],"height:1.2em;vertical-align:-0.35em;",[569,1620,1569],{"className":1621},[746],[569,1623],{"className":1624,"style":819},[818],[569,1626,1628,1635,1638,1641,1644,1647,1719],{"className":1627},[823],[569,1629,1631],{"className":1630,"style":832},[830,831],[569,1632,699],{"className":1633},[836,1634],"size1",[569,1636,703],{"className":1637},[612],[569,1639],{"className":1640,"style":844},[818],[569,1642,706],{"className":1643},[848],[569,1645],{"className":1646,"style":844},[818],[569,1648,1650,1653,1716],{"className":1649},[612],[569,1651],{"className":1652},[830,858],[569,1654,1656],{"className":1655},[708],[569,1657,1659,1707],{"className":1658},[751,752],[569,1660,1662,1704],{"className":1661},[756],[569,1663,1666,1681,1689],{"className":1664,"style":1665},[760],"height:0.7475em;",[569,1667,1669,1672],{"style":1668},"top:-2.655em;",[569,1670],{"className":1671,"style":769},[768],[569,1673,1675],{"className":1674},[773,774,775,776],[569,1676,1678],{"className":1677},[612,776],[569,1679,1367],{"className":1680},[612,776],[569,1682,1683,1686],{"style":886},[569,1684],{"className":1685,"style":769},[768],[569,1687],{"className":1688,"style":894},[893],[569,1690,1692,1695],{"style":1691},"top:-3.4461em;",[569,1693],{"className":1694,"style":769},[768],[569,1696,1698],{"className":1697},[773,774,775,776],[569,1699,1701],{"className":1700},[612,776],[569,1702,565],{"className":1703},[612,613,776],[569,1705,805],{"className":1706},[804],[569,1708,1710],{"className":1709},[756],[569,1711,1714],{"className":1712,"style":1713},[760],"height:0.345em;",[569,1715],{},[569,1717],{"className":1718},[923,858],[569,1720,1722],{"className":1721,"style":832},[923,831],[569,1723,717],{"className":1724},[836,1634],[1323,1726,1727,1728,1518],{},"Verdopplungszeit: ",[569,1729,1731,1764],{"className":1730},[572],[569,1732,1734],{"className":1733},[576],[578,1735,1736],{"xmlns":580},[582,1737,1738,1761],{},[585,1739,1740,1747,1749],{},[1033,1741,1742,1744],{},[588,1743,1027],{},[701,1745,1746],{},"2",[678,1748,722],{},[708,1750,1751,1759],{},[585,1752,1753,1755,1757],{},[588,1754,1569],{},[678,1756,680],{},[701,1758,1746],{},[588,1760,712],{},[592,1762,1763],{"encoding":594},"t_2 = \\frac{\\ln 2}{r}",[569,1765,1767,1823],{"className":1766,"ariaHidden":599},[598],[569,1768,1770,1774,1814,1817,1820],{"className":1769},[603],[569,1771],{"className":1772,"style":1773},[607],"height:0.7651em;vertical-align:-0.15em;",[569,1775,1777,1780],{"className":1776},[612],[569,1778,1027],{"className":1779},[612,613],[569,1781,1783],{"className":1782},[933],[569,1784,1786,1806],{"className":1785},[751,752],[569,1787,1789,1803],{"className":1788},[756],[569,1790,1792],{"className":1791,"style":1110},[760],[569,1793,1794,1797],{"style":1402},[569,1795],{"className":1796,"style":950},[768],[569,1798,1800],{"className":1799},[773,774,775,776],[569,1801,1746],{"className":1802},[612,776],[569,1804,805],{"className":1805},[804],[569,1807,1809],{"className":1808},[756],[569,1810,1812],{"className":1811,"style":1132},[760],[569,1813],{},[569,1815],{"className":1816,"style":960},[818],[569,1818,722],{"className":1819},[786],[569,1821],{"className":1822,"style":960},[818],[569,1824,1826,1830],{"className":1825},[603],[569,1827],{"className":1828,"style":1829},[607],"height:1.2251em;vertical-align:-0.345em;",[569,1831,1833,1836,1912],{"className":1832},[612],[569,1834],{"className":1835},[830,858],[569,1837,1839],{"className":1838},[708],[569,1840,1842,1904],{"className":1841},[751,752],[569,1843,1845,1901],{"className":1844},[756],[569,1846,1849,1863,1871],{"className":1847,"style":1848},[760],"height:0.8801em;",[569,1850,1851,1854],{"style":1668},[569,1852],{"className":1853,"style":769},[768],[569,1855,1857],{"className":1856},[773,774,775,776],[569,1858,1860],{"className":1859},[612,776],[569,1861,712],{"className":1862,"style":907},[612,613,776],[569,1864,1865,1868],{"style":886},[569,1866],{"className":1867,"style":769},[768],[569,1869],{"className":1870,"style":894},[893],[569,1872,1874,1877],{"style":1873},"top:-3.394em;",[569,1875],{"className":1876,"style":769},[768],[569,1878,1880],{"className":1879},[773,774,775,776],[569,1881,1883,1894,1898],{"className":1882},[612,776],[569,1884,1886,1890],{"className":1885},[746,776],[569,1887,1889],{"className":1888},[776],"l",[569,1891,1893],{"className":1892},[776],"n",[569,1895],{"className":1896,"style":1897},[818,776],"margin-right:0.1952em;",[569,1899,1746],{"className":1900},[612,776],[569,1902,805],{"className":1903},[804],[569,1905,1907],{"className":1906},[756],[569,1908,1910],{"className":1909,"style":1713},[760],[569,1911],{},[569,1913],{"className":1914},[923,858],[565,1916,1917,1918,1987],{},"Stetige Verzinsung wird vor allem in der Finanzmathematik verwendet, z.B. für die Bewertung von Anleihen und Optionen, weil sich mit ",[569,1919,1921,1943],{"className":1920},[572],[569,1922,1924],{"className":1923},[576],[578,1925,1926],{"xmlns":580},[582,1927,1928,1940],{},[585,1929,1930],{},[693,1931,1932,1934],{},[588,1933,727],{},[585,1935,1936,1938],{},[588,1937,712],{},[588,1939,1027],{},[592,1941,1942],{"encoding":594},"e^{rt}",[569,1944,1946],{"className":1945,"ariaHidden":599},[598],[569,1947,1949,1952],{"className":1948},[603],[569,1950],{"className":1951,"style":1153},[607],[569,1953,1955,1958],{"className":1954},[612],[569,1956,727],{"className":1957},[612,613],[569,1959,1961],{"className":1960},[933],[569,1962,1964],{"className":1963},[751],[569,1965,1967],{"className":1966},[756],[569,1968,1970],{"className":1969,"style":1153},[760],[569,1971,1972,1975],{"style":1156},[569,1973],{"className":1974,"style":950},[768],[569,1976,1978],{"className":1977},[773,774,775,776],[569,1979,1981,1984],{"className":1980},[612,776],[569,1982,712],{"className":1983,"style":907},[612,613,776],[569,1985,1027],{"className":1986},[612,613,776]," leichter rechnen lässt.",[560,1989,1991],{"id":1990},"beispiele","Beispiele",[565,1993,1994,2023,2024,2053,2054,2119],{},[569,1995,1997,2011],{"className":1996},[572],[569,1998,2000],{"className":1999},[576],[578,2001,2002],{"xmlns":580},[582,2003,2004,2009],{},[585,2005,2006],{},[701,2007,2008],{},"1000",[592,2010,2008],{"encoding":594},[569,2012,2014],{"className":2013,"ariaHidden":599},[598],[569,2015,2017,2020],{"className":2016},[603],[569,2018],{"className":2019,"style":1514},[607],[569,2021,2008],{"className":2022},[612]," € werden ",[569,2025,2027,2041],{"className":2026},[572],[569,2028,2030],{"className":2029},[576],[578,2031,2032],{"xmlns":580},[582,2033,2034,2039],{},[585,2035,2036],{},[701,2037,2038],{},"10",[592,2040,2038],{"encoding":594},[569,2042,2044],{"className":2043,"ariaHidden":599},[598],[569,2045,2047,2050],{"className":2046},[603],[569,2048],{"className":2049,"style":1514},[607],[569,2051,2038],{"className":2052},[612]," Jahre lang mit ",[569,2055,2057,2076],{"className":2056},[572],[569,2058,2060],{"className":2059},[576],[578,2061,2062],{"xmlns":580},[582,2063,2064,2073],{},[585,2065,2066,2068,2070],{},[588,2067,712],{},[678,2069,722],{},[701,2071,2072],{},"0,05",[592,2074,2075],{"encoding":594},"r = 0{,}05",[569,2077,2079,2097],{"className":2078,"ariaHidden":599},[598],[569,2080,2082,2085,2088,2091,2094],{"className":2081},[603],[569,2083],{"className":2084,"style":608},[607],[569,2086,712],{"className":2087,"style":907},[612,613],[569,2089],{"className":2090,"style":960},[818],[569,2092,722],{"className":2093},[786],[569,2095],{"className":2096,"style":960},[818],[569,2098,2100,2104,2107,2115],{"className":2099},[603],[569,2101],{"className":2102,"style":2103},[607],"height:0.8389em;vertical-align:-0.1944em;",[569,2105,1039],{"className":2106},[612],[569,2108,2110],{"className":2109},[612],[569,2111,2114],{"className":2112},[2113],"mpunct",",",[569,2116,2118],{"className":2117},[612],"05"," stetig verzinst:",[569,2121,2123],{"className":2122},[655],[569,2124,2126,2189],{"className":2125},[572],[569,2127,2129],{"className":2128},[576],[578,2130,2131],{"xmlns":580,"display":664},[582,2132,2133,2186],{},[585,2134,2135,2137,2139,2141,2143,2145,2147,2149,2161,2163,2165,2167,2174,2177,2180,2183],{},[588,2136,1021],{},[678,2138,699],{"stretchy":1024},[701,2140,2038],{},[678,2142,717],{"stretchy":1024},[678,2144,722],{},[701,2146,2008],{},[678,2148,1205],{},[693,2150,2151,2153],{},[588,2152,727],{},[585,2154,2155,2157,2159],{},[701,2156,2072],{},[678,2158,1205],{},[701,2160,2038],{},[678,2162,722],{},[701,2164,2008],{},[678,2166,1205],{},[693,2168,2169,2171],{},[588,2170,727],{},[701,2172,2173],{},"0,5",[678,2175,2176],{},"≈",[701,2178,2179],{},"1648,72",[1343,2181,2182],{}," ",[1343,2184,2185],{},"Euro",[592,2187,2188],{"encoding":594},"K(10) = 1000 \\cdot e^{0{,}05 \\cdot 10} = 1000 \\cdot e^{0{,}5} \\approx 1648{,}72\\,\\text{Euro}",[569,2190,2192,2219,2237,2300,2318,2375],{"className":2191,"ariaHidden":599},[598],[569,2193,2195,2198,2201,2204,2207,2210,2213,2216],{"className":2194},[603],[569,2196],{"className":2197,"style":1062},[607],[569,2199,1021],{"className":2200,"style":1066},[612,613],[569,2202,699],{"className":2203},[830],[569,2205,2038],{"className":2206},[612],[569,2208,717],{"className":2209},[923],[569,2211],{"className":2212,"style":960},[818],[569,2214,722],{"className":2215},[786],[569,2217],{"className":2218,"style":960},[818],[569,2220,2222,2225,2228,2231,2234],{"className":2221},[603],[569,2223],{"className":2224,"style":1514},[607],[569,2226,2008],{"className":2227},[612],[569,2229],{"className":2230,"style":844},[818],[569,2232,1205],{"className":2233},[848],[569,2235],{"className":2236,"style":844},[818],[569,2238,2240,2244,2291,2294,2297],{"className":2239},[603],[569,2241],{"className":2242,"style":2243},[607],"height:0.8641em;",[569,2245,2247,2250],{"className":2246},[612],[569,2248,727],{"className":2249},[612,613],[569,2251,2253],{"className":2252},[933],[569,2254,2256],{"className":2255},[751],[569,2257,2259],{"className":2258},[756],[569,2260,2262],{"className":2261,"style":2243},[760],[569,2263,2264,2267],{"style":994},[569,2265],{"className":2266,"style":950},[768],[569,2268,2270],{"className":2269},[773,774,775,776],[569,2271,2273,2276,2282,2285,2288],{"className":2272},[612,776],[569,2274,1039],{"className":2275},[612,776],[569,2277,2279],{"className":2278},[612,776],[569,2280,2114],{"className":2281},[2113,776],[569,2283,2118],{"className":2284},[612,776],[569,2286,1205],{"className":2287},[848,776],[569,2289,2038],{"className":2290},[612,776],[569,2292],{"className":2293,"style":960},[818],[569,2295,722],{"className":2296},[786],[569,2298],{"className":2299,"style":960},[818],[569,2301,2303,2306,2309,2312,2315],{"className":2302},[603],[569,2304],{"className":2305,"style":1514},[607],[569,2307,2008],{"className":2308},[612],[569,2310],{"className":2311,"style":844},[818],[569,2313,1205],{"className":2314},[848],[569,2316],{"className":2317,"style":844},[818],[569,2319,2321,2324,2366,2369,2372],{"className":2320},[603],[569,2322],{"className":2323,"style":2243},[607],[569,2325,2327,2330],{"className":2326},[612],[569,2328,727],{"className":2329},[612,613],[569,2331,2333],{"className":2332},[933],[569,2334,2336],{"className":2335},[751],[569,2337,2339],{"className":2338},[756],[569,2340,2342],{"className":2341,"style":2243},[760],[569,2343,2344,2347],{"style":994},[569,2345],{"className":2346,"style":950},[768],[569,2348,2350],{"className":2349},[773,774,775,776],[569,2351,2353,2356,2362],{"className":2352},[612,776],[569,2354,1039],{"className":2355},[612,776],[569,2357,2359],{"className":2358},[612,776],[569,2360,2114],{"className":2361},[2113,776],[569,2363,2365],{"className":2364},[612,776],"5",[569,2367],{"className":2368,"style":960},[818],[569,2370,2176],{"className":2371},[786],[569,2373],{"className":2374,"style":960},[818],[569,2376,2378,2382,2386,2392,2396,2399],{"className":2377},[603],[569,2379],{"className":2380,"style":2381},[607],"height:0.8778em;vertical-align:-0.1944em;",[569,2383,2385],{"className":2384},[612],"1648",[569,2387,2389],{"className":2388},[612],[569,2390,2114],{"className":2391},[2113],[569,2393,2395],{"className":2394},[612],"72",[569,2397],{"className":2398,"style":819},[818],[569,2400,2402],{"className":2401},[612,1415],[569,2403,2185],{"className":2404},[612],[565,2406,2407,2408,2541,2542,1518],{},"Mit jährlicher Gutschrift wären es ",[569,2409,2411,2439],{"className":2410},[572],[569,2412,2414],{"className":2413},[576],[578,2415,2416],{"xmlns":580},[582,2417,2418,2436],{},[585,2419,2420,2422,2424,2431,2433],{},[701,2421,2008],{},[678,2423,1205],{},[693,2425,2426,2429],{},[701,2427,2428],{},"1,05",[701,2430,2038],{},[678,2432,2176],{},[701,2434,2435],{},"1628,89",[592,2437,2438],{"encoding":594},"1000 \\cdot 1{,}05^{10} \\approx 1628{,}89",[569,2440,2442,2460,2521],{"className":2441,"ariaHidden":599},[598],[569,2443,2445,2448,2451,2454,2457],{"className":2444},[603],[569,2446],{"className":2447,"style":1514},[607],[569,2449,2008],{"className":2450},[612],[569,2452],{"className":2453,"style":844},[818],[569,2455,1205],{"className":2456},[848],[569,2458],{"className":2459,"style":844},[818],[569,2461,2463,2467,2470,2476,2479,2512,2515,2518],{"className":2462},[603],[569,2464],{"className":2465,"style":2466},[607],"height:1.0085em;vertical-align:-0.1944em;",[569,2468,703],{"className":2469},[612],[569,2471,2473],{"className":2472},[612],[569,2474,2114],{"className":2475},[2113],[569,2477,1039],{"className":2478},[612],[569,2480,2482,2485],{"className":2481},[612],[569,2483,2365],{"className":2484},[612],[569,2486,2488],{"className":2487},[933],[569,2489,2491],{"className":2490},[751],[569,2492,2494],{"className":2493},[756],[569,2495,2498],{"className":2496,"style":2497},[760],"height:0.8141em;",[569,2499,2500,2503],{"style":1156},[569,2501],{"className":2502,"style":950},[768],[569,2504,2506],{"className":2505},[773,774,775,776],[569,2507,2509],{"className":2508},[612,776],[569,2510,2038],{"className":2511},[612,776],[569,2513],{"className":2514,"style":960},[818],[569,2516,2176],{"className":2517},[786],[569,2519],{"className":2520,"style":960},[818],[569,2522,2524,2527,2531,2537],{"className":2523},[603],[569,2525],{"className":2526,"style":2103},[607],[569,2528,2530],{"className":2529},[612],"1628",[569,2532,2534],{"className":2533},[612],[569,2535,2114],{"className":2536},[2113],[569,2538,2540],{"className":2539},[612],"89"," €. Der effektive Jahreszins der stetigen Verzinsung ist ",[569,2543,2545,2585],{"className":2544},[572],[569,2546,2548],{"className":2547},[576],[578,2549,2550],{"xmlns":580},[582,2551,2552,2582],{},[585,2553,2554,2556,2562,2564,2566,2568,2570,2572,2574,2577,2579],{},[678,2555,699],{"stretchy":1024},[693,2557,2558,2560],{},[588,2559,727],{},[701,2561,2072],{},[678,2563,1358],{},[701,2565,703],{},[678,2567,717],{"stretchy":1024},[678,2569,1205],{},[701,2571,1367],{},[678,2573,2176],{},[701,2575,2576],{},"5,127",[1343,2578,2182],{},[588,2580,2581],{"mathvariant":690},"%",[592,2583,2584],{"encoding":594},"(e^{0{,}05} - 1) \\cdot 100 \\approx 5{,}127\\,\\%",[569,2586,2588,2648,2669,2687],{"className":2587,"ariaHidden":599},[598],[569,2589,2591,2595,2598,2639,2642,2645],{"className":2590},[603],[569,2592],{"className":2593,"style":2594},[607],"height:1.0641em;vertical-align:-0.25em;",[569,2596,699],{"className":2597},[830],[569,2599,2601,2604],{"className":2600},[612],[569,2602,727],{"className":2603},[612,613],[569,2605,2607],{"className":2606},[933],[569,2608,2610],{"className":2609},[751],[569,2611,2613],{"className":2612},[756],[569,2614,2616],{"className":2615,"style":2497},[760],[569,2617,2618,2621],{"style":1156},[569,2619],{"className":2620,"style":950},[768],[569,2622,2624],{"className":2623},[773,774,775,776],[569,2625,2627,2630,2636],{"className":2626},[612,776],[569,2628,1039],{"className":2629},[612,776],[569,2631,2633],{"className":2632},[612,776],[569,2634,2114],{"className":2635},[2113,776],[569,2637,2118],{"className":2638},[612,776],[569,2640],{"className":2641,"style":844},[818],[569,2643,1358],{"className":2644},[848],[569,2646],{"className":2647,"style":844},[818],[569,2649,2651,2654,2657,2660,2663,2666],{"className":2650},[603],[569,2652],{"className":2653,"style":1062},[607],[569,2655,703],{"className":2656},[612],[569,2658,717],{"className":2659},[923],[569,2661],{"className":2662,"style":844},[818],[569,2664,1205],{"className":2665},[848],[569,2667],{"className":2668,"style":844},[818],[569,2670,2672,2675,2678,2681,2684],{"className":2671},[603],[569,2673],{"className":2674,"style":1514},[607],[569,2676,1367],{"className":2677},[612],[569,2679],{"className":2680,"style":960},[818],[569,2682,2176],{"className":2683},[786],[569,2685],{"className":2686,"style":960},[818],[569,2688,2690,2694,2697,2703,2707,2710],{"className":2689},[603],[569,2691],{"className":2692,"style":2693},[607],"height:0.9444em;vertical-align:-0.1944em;",[569,2695,2365],{"className":2696},[612],[569,2698,2700],{"className":2699},[612],[569,2701,2114],{"className":2702},[2113],[569,2704,2706],{"className":2705},[612],"127",[569,2708],{"className":2709,"style":819},[818],[569,2711,2581],{"className":2712},[612],[565,2714,2715,2716,2775],{},"Verdopplungszeit bei ",[569,2717,2719,2736],{"className":2718},[572],[569,2720,2722],{"className":2721},[576],[578,2723,2724],{"xmlns":580},[582,2725,2726,2734],{},[585,2727,2728,2730,2732],{},[588,2729,712],{},[678,2731,722],{},[701,2733,2072],{},[592,2735,2075],{"encoding":594},[569,2737,2739,2757],{"className":2738,"ariaHidden":599},[598],[569,2740,2742,2745,2748,2751,2754],{"className":2741},[603],[569,2743],{"className":2744,"style":608},[607],[569,2746,712],{"className":2747,"style":907},[612,613],[569,2749],{"className":2750,"style":960},[818],[569,2752,722],{"className":2753},[786],[569,2755],{"className":2756,"style":960},[818],[569,2758,2760,2763,2766,2772],{"className":2759},[603],[569,2761],{"className":2762,"style":2103},[607],[569,2764,1039],{"className":2765},[612],[569,2767,2769],{"className":2768},[612],[569,2770,2114],{"className":2771},[2113],[569,2773,2118],{"className":2774},[612],":",[569,2777,2779],{"className":2778},[655],[569,2780,2782,2822],{"className":2781},[572],[569,2783,2785],{"className":2784},[576],[578,2786,2787],{"xmlns":580,"display":664},[582,2788,2789,2819],{},[585,2790,2791,2797,2799,2811,2813,2816],{},[1033,2792,2793,2795],{},[588,2794,1027],{},[701,2796,1746],{},[678,2798,722],{},[708,2800,2801,2809],{},[585,2802,2803,2805,2807],{},[588,2804,1569],{},[678,2806,680],{},[701,2808,1746],{},[701,2810,2072],{},[678,2812,2176],{},[701,2814,2815],{},"13,86",[1343,2817,2818],{}," Jahre",[592,2820,2821],{"encoding":594},"t_2 = \\frac{\\ln 2}{0{,}05} \\approx 13{,}86 \\text{ Jahre}",[569,2823,2825,2880,2975],{"className":2824,"ariaHidden":599},[598],[569,2826,2828,2831,2871,2874,2877],{"className":2827},[603],[569,2829],{"className":2830,"style":1773},[607],[569,2832,2834,2837],{"className":2833},[612],[569,2835,1027],{"className":2836},[612,613],[569,2838,2840],{"className":2839},[933],[569,2841,2843,2863],{"className":2842},[751,752],[569,2844,2846,2860],{"className":2845},[756],[569,2847,2849],{"className":2848,"style":1110},[760],[569,2850,2851,2854],{"style":1402},[569,2852],{"className":2853,"style":950},[768],[569,2855,2857],{"className":2856},[773,774,775,776],[569,2858,1746],{"className":2859},[612,776],[569,2861,805],{"className":2862},[804],[569,2864,2866],{"className":2865},[756],[569,2867,2869],{"className":2868,"style":1132},[760],[569,2870],{},[569,2872],{"className":2873,"style":960},[818],[569,2875,722],{"className":2876},[786],[569,2878],{"className":2879,"style":960},[818],[569,2881,2883,2887,2966,2969,2972],{"className":2882},[603],[569,2884],{"className":2885,"style":2886},[607],"height:2.2519em;vertical-align:-0.8804em;",[569,2888,2890,2893,2963],{"className":2889},[612],[569,2891],{"className":2892},[830,858],[569,2894,2896],{"className":2895},[708],[569,2897,2899,2954],{"className":2898},[751,752],[569,2900,2902,2951],{"className":2901},[756],[569,2903,2906,2926,2934],{"className":2904,"style":2905},[760],"height:1.3714em;",[569,2907,2908,2911],{"style":874},[569,2909],{"className":2910,"style":769},[768],[569,2912,2914,2917,2923],{"className":2913},[612],[569,2915,1039],{"className":2916},[612],[569,2918,2920],{"className":2919},[612],[569,2921,2114],{"className":2922},[2113],[569,2924,2118],{"className":2925},[612],[569,2927,2928,2931],{"style":886},[569,2929],{"className":2930,"style":769},[768],[569,2932],{"className":2933,"style":894},[893],[569,2935,2936,2939],{"style":897},[569,2937],{"className":2938,"style":769},[768],[569,2940,2942,2945,2948],{"className":2941},[612],[569,2943,1569],{"className":2944},[746],[569,2946],{"className":2947,"style":819},[818],[569,2949,1746],{"className":2950},[612],[569,2952,805],{"className":2953},[804],[569,2955,2957],{"className":2956},[756],[569,2958,2961],{"className":2959,"style":2960},[760],"height:0.8804em;",[569,2962],{},[569,2964],{"className":2965},[923,858],[569,2967],{"className":2968,"style":960},[818],[569,2970,2176],{"className":2971},[786],[569,2973],{"className":2974,"style":960},[818],[569,2976,2978,2982,2986,2992,2996],{"className":2977},[603],[569,2979],{"className":2980,"style":2981},[607],"height:0.8889em;vertical-align:-0.1944em;",[569,2983,2985],{"className":2984},[612],"13",[569,2987,2989],{"className":2988},[612],[569,2990,2114],{"className":2991},[2113],[569,2993,2995],{"className":2994},[612],"86",[569,2997,2999],{"className":2998},[612,1415],[569,3000,2818],{"className":3001},[612],[565,3003,3004,3005,3045,3046,3134,3135,1518],{},"Umgekehrt entsprechen ",[569,3006,3008,3026],{"className":3007},[572],[569,3009,3011],{"className":3010},[576],[578,3012,3013],{"xmlns":580},[582,3014,3015,3023],{},[585,3016,3017,3019,3021],{},[701,3018,2365],{},[1343,3020,2182],{},[588,3022,2581],{"mathvariant":690},[592,3024,3025],{"encoding":594},"5\\,\\%",[569,3027,3029],{"className":3028,"ariaHidden":599},[598],[569,3030,3032,3036,3039,3042],{"className":3031},[603],[569,3033],{"className":3034,"style":3035},[607],"height:0.8056em;vertical-align:-0.0556em;",[569,3037,2365],{"className":3038},[612],[569,3040],{"className":3041,"style":819},[818],[569,3043,2581],{"className":3044},[612]," mit jährlicher Gutschrift einem stetigen Zinssatz von ",[569,3047,3049,3076],{"className":3048},[572],[569,3050,3052],{"className":3051},[576],[578,3053,3054],{"xmlns":580},[582,3055,3056,3073],{},[585,3057,3058,3060,3062,3064,3066,3068,3070],{},[588,3059,1569],{},[678,3061,680],{},[678,3063,699],{"stretchy":1024},[701,3065,2428],{},[678,3067,717],{"stretchy":1024},[678,3069,2176],{},[701,3071,3072],{},"0,04879",[592,3074,3075],{"encoding":594},"\\ln(1{,}05) \\approx 0{,}04879",[569,3077,3079,3115],{"className":3078,"ariaHidden":599},[598],[569,3080,3082,3085,3088,3091,3094,3100,3103,3106,3109,3112],{"className":3081},[603],[569,3083],{"className":3084,"style":1062},[607],[569,3086,1569],{"className":3087},[746],[569,3089,699],{"className":3090},[830],[569,3092,703],{"className":3093},[612],[569,3095,3097],{"className":3096},[612],[569,3098,2114],{"className":3099},[2113],[569,3101,2118],{"className":3102},[612],[569,3104,717],{"className":3105},[923],[569,3107],{"className":3108,"style":960},[818],[569,3110,2176],{"className":3111},[786],[569,3113],{"className":3114,"style":960},[818],[569,3116,3118,3121,3124,3130],{"className":3117},[603],[569,3119],{"className":3120,"style":2103},[607],[569,3122,1039],{"className":3123},[612],[569,3125,3127],{"className":3126},[612],[569,3128,2114],{"className":3129},[2113],[569,3131,3133],{"className":3132},[612],"04879",", also etwa ",[569,3136,3138,3157],{"className":3137},[572],[569,3139,3141],{"className":3140},[576],[578,3142,3143],{"xmlns":580},[582,3144,3145,3154],{},[585,3146,3147,3150,3152],{},[701,3148,3149],{},"4,879",[1343,3151,2182],{},[588,3153,2581],{"mathvariant":690},[592,3155,3156],{"encoding":594},"4{,}879\\,\\%",[569,3158,3160],{"className":3159,"ariaHidden":599},[598],[569,3161,3163,3166,3170,3176,3180,3183],{"className":3162},[603],[569,3164],{"className":3165,"style":2693},[607],[569,3167,3169],{"className":3168},[612],"4",[569,3171,3173],{"className":3172},[612],[569,3174,2114],{"className":3175},[2113],[569,3177,3179],{"className":3178},[612],"879",[569,3181],{"className":3182,"style":819},[818],[569,3184,2581],{"className":3185},[612],[560,3187,3189],{"id":3188},"typische-fehler","Typische Fehler",[1320,3191,3192,3353,3455],{},[1323,3193,3194,3195,3269,3270,1518],{},"Den Zinssatz in Prozent einsetzen: ",[569,3196,3198,3222],{"className":3197},[572],[569,3199,3201],{"className":3200},[576],[578,3202,3203],{"xmlns":580},[582,3204,3205,3219],{},[585,3206,3207],{},[693,3208,3209,3211],{},[588,3210,727],{},[585,3212,3213,3215,3217],{},[701,3214,2365],{},[678,3216,1205],{},[701,3218,2038],{},[592,3220,3221],{"encoding":594},"e^{5 \\cdot 10}",[569,3223,3225],{"className":3224,"ariaHidden":599},[598],[569,3226,3228,3231],{"className":3227},[603],[569,3229],{"className":3230,"style":2497},[607],[569,3232,3234,3237],{"className":3233},[612],[569,3235,727],{"className":3236},[612,613],[569,3238,3240],{"className":3239},[933],[569,3241,3243],{"className":3242},[751],[569,3244,3246],{"className":3245},[756],[569,3247,3249],{"className":3248,"style":2497},[760],[569,3250,3251,3254],{"style":1156},[569,3252],{"className":3253,"style":950},[768],[569,3255,3257],{"className":3256},[773,774,775,776],[569,3258,3260,3263,3266],{"className":3259},[612,776],[569,3261,2365],{"className":3262},[612,776],[569,3264,1205],{"className":3265},[848,776],[569,3267,2038],{"className":3268},[612,776]," statt ",[569,3271,3273,3297],{"className":3272},[572],[569,3274,3276],{"className":3275},[576],[578,3277,3278],{"xmlns":580},[582,3279,3280,3294],{},[585,3281,3282],{},[693,3283,3284,3286],{},[588,3285,727],{},[585,3287,3288,3290,3292],{},[701,3289,2072],{},[678,3291,1205],{},[701,3293,2038],{},[592,3295,3296],{"encoding":594},"e^{0{,}05 \\cdot 10}",[569,3298,3300],{"className":3299,"ariaHidden":599},[598],[569,3301,3303,3306],{"className":3302},[603],[569,3304],{"className":3305,"style":2497},[607],[569,3307,3309,3312],{"className":3308},[612],[569,3310,727],{"className":3311},[612,613],[569,3313,3315],{"className":3314},[933],[569,3316,3318],{"className":3317},[751],[569,3319,3321],{"className":3320},[756],[569,3322,3324],{"className":3323,"style":2497},[760],[569,3325,3326,3329],{"style":1156},[569,3327],{"className":3328,"style":950},[768],[569,3330,3332],{"className":3331},[773,774,775,776],[569,3333,3335,3338,3344,3347,3350],{"className":3334},[612,776],[569,3336,1039],{"className":3337},[612,776],[569,3339,3341],{"className":3340},[612,776],[569,3342,2114],{"className":3343},[2113,776],[569,3345,2118],{"className":3346},[612,776],[569,3348,1205],{"className":3349},[848,776],[569,3351,2038],{"className":3352},[612,776],[1323,3354,3355,3356,3415,3416,3454],{},"Stetigen und jährlichen Zinssatz gleichsetzen. ",[569,3357,3359,3376],{"className":3358},[572],[569,3360,3362],{"className":3361},[576],[578,3363,3364],{"xmlns":580},[582,3365,3366,3374],{},[585,3367,3368,3370,3372],{},[588,3369,712],{},[678,3371,722],{},[701,3373,2072],{},[592,3375,2075],{"encoding":594},[569,3377,3379,3397],{"className":3378,"ariaHidden":599},[598],[569,3380,3382,3385,3388,3391,3394],{"className":3381},[603],[569,3383],{"className":3384,"style":608},[607],[569,3386,712],{"className":3387,"style":907},[612,613],[569,3389],{"className":3390,"style":960},[818],[569,3392,722],{"className":3393},[786],[569,3395],{"className":3396,"style":960},[818],[569,3398,3400,3403,3406,3412],{"className":3399},[603],[569,3401],{"className":3402,"style":2103},[607],[569,3404,1039],{"className":3405},[612],[569,3407,3409],{"className":3408},[612],[569,3410,2114],{"className":3411},[2113],[569,3413,2118],{"className":3414},[612]," stetig liefert mehr als ",[569,3417,3419,3436],{"className":3418},[572],[569,3420,3422],{"className":3421},[576],[578,3423,3424],{"xmlns":580},[582,3425,3426,3434],{},[585,3427,3428,3430,3432],{},[701,3429,2365],{},[1343,3431,2182],{},[588,3433,2581],{"mathvariant":690},[592,3435,3025],{"encoding":594},[569,3437,3439],{"className":3438,"ariaHidden":599},[598],[569,3440,3442,3445,3448,3451],{"className":3441},[603],[569,3443],{"className":3444,"style":3035},[607],[569,3446,2365],{"className":3447},[612],[569,3449],{"className":3450,"style":819},[818],[569,3452,2581],{"className":3453},[612]," jährlich.",[1323,3456,3457,3458,3517,3518,1518],{},"Die stetige Verzinsung für unbegrenzt ertragreich halten. Auch bei unendlich vielen Gutschriften bleibt der Effektivzins endlich, bei ",[569,3459,3461,3478],{"className":3460},[572],[569,3462,3464],{"className":3463},[576],[578,3465,3466],{"xmlns":580},[582,3467,3468,3476],{},[585,3469,3470,3472,3474],{},[588,3471,712],{},[678,3473,722],{},[701,3475,2072],{},[592,3477,2075],{"encoding":594},[569,3479,3481,3499],{"className":3480,"ariaHidden":599},[598],[569,3482,3484,3487,3490,3493,3496],{"className":3483},[603],[569,3485],{"className":3486,"style":608},[607],[569,3488,712],{"className":3489,"style":907},[612,613],[569,3491],{"className":3492,"style":960},[818],[569,3494,722],{"className":3495},[786],[569,3497],{"className":3498,"style":960},[818],[569,3500,3502,3505,3508,3514],{"className":3501},[603],[569,3503],{"className":3504,"style":2103},[607],[569,3506,1039],{"className":3507},[612],[569,3509,3511],{"className":3510},[612],[569,3512,2114],{"className":3513},[2113],[569,3515,2118],{"className":3516},[612]," etwa ",[569,3519,3521,3539],{"className":3520},[572],[569,3522,3524],{"className":3523},[576],[578,3525,3526],{"xmlns":580},[582,3527,3528,3536],{},[585,3529,3530,3532,3534],{},[701,3531,2576],{},[1343,3533,2182],{},[588,3535,2581],{"mathvariant":690},[592,3537,3538],{"encoding":594},"5{,}127\\,\\%",[569,3540,3542],{"className":3541,"ariaHidden":599},[598],[569,3543,3545,3548,3551,3557,3560,3563],{"className":3544},[603],[569,3546],{"className":3547,"style":2693},[607],[569,3549,2365],{"className":3550},[612],[569,3552,3554],{"className":3553},[612],[569,3555,2114],{"className":3556},[2113],[569,3558,2706],{"className":3559},[612],[569,3561],{"className":3562,"style":819},[818],[569,3564,2581],{"className":3565},[612],{"title":3567,"searchDepth":3568,"depth":3568,"links":3569},"",2,[3570,3571,3572],{"id":562,"depth":3568,"text":563},{"id":1990,"depth":3568,"text":1991},{"id":3188,"depth":3568,"text":3189},[3574,3577,3580,3583,3586,3589,3592],{"lhs":3575,"rhs":3576},"round((1 + 0.05\u002F1000000)^1000000, 6)","round(exp(0.05), 6)",{"lhs":3578,"rhs":3579},"K*exp(r*(t + s))","K*exp(r*t)*exp(r*s)",{"lhs":3581,"rhs":3582},"round(1000*exp(0.05*10), 2)","1648.72",{"lhs":3584,"rhs":3585},"round(1000*1.05^10, 2)","1628.89",{"lhs":3587,"rhs":3588},"round((exp(0.05) - 1)*100, 3)","5.127",{"lhs":3590,"rhs":3591},"round(log(2)\u002F0.05, 2)","13.86",{"lhs":3593,"rhs":3594},"round(log(1.05)*100, 3)","4.879","r \\in \\mathbb{R},\\ t \\geq 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>r\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">r \\in \\mathbb{R},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\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\">R\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>t\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">t \\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:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">t\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","continuous-compounding","K(t) = K_0 \\cdot e^{r t} = \\lim_{m \\to \\infty} K_0 \\cdot \\left(1 + \\frac{r}{m}\\right)^{m t}","\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>\u003Cmi>K\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>t\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>K\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsup>\u003Cmi>e\u003C\u002Fmi>\u003Cmrow>\u003Cmi>r\u003C\u002Fmi>\u003Cmi>t\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmunder>\u003Cmrow>\u003Cmi>lim\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>m\u003C\u002Fmi>\u003Cmo>→\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmunder>\u003Cmsub>\u003Cmi>K\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsup>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>+\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>r\u003C\u002Fmi>\u003Cmi>m\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>m\u003C\u002Fmi>\u003Cmi>t\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">K(t) = K_0 \\cdot e^{r t} = \\lim_{m \\to \\infty} K_0 \\cdot \\left(1 + \\frac{r}{m}\\right)^{m t}\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">K\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">t\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">K\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0715em;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\">0\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:0.2222em;\">\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:0.8436em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">e\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8436em;\">\u003Cspan style=\"top:-3.113em;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 mathnormal mtight\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">t\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:1.3944em;vertical-align:-0.7em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6944em;\">\u003Cspan style=\"top:-2.4em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">m\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">→\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">∞\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop\">lim\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:0.7em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">K\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0715em;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\">0\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:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0195em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\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 mathnormal\">m\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\" style=\"margin-right:0.0278em;\">r\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>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3335em;\">\u003Cspan style=\"top:-3.6029em;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 mathnormal mtight\">m\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">t\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Farithmetic\u002Fstetige-verzinsung",[],[3608,3609,3610,3611],"compound-interest","effective-interest-rate","euler-number-limit","natural-exponential-function",{"title":548,"description":3567},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fstetige-verzinsung","Bei stetiger Verzinsung wächst ein Kapital wie K₀ · e^(rt), der Grenzfall unendlich häufiger Zinsgutschrift.",[3616,3617,3618,3619,3620],"zinsen","exponentialfunktion","eulersche zahl","grenzwert","finanzmathematik",[3622,3626,3630,3633,3636,3639],{"symbol":3623,"meaning":3624,"symbolHtml":3625},"K(t)","Kapital zum Zeitpunkt t","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>K\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>t\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">K(t)\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">K\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">t\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3627,"meaning":3628,"symbolHtml":3629},"K_0","Anfangskapital","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>K\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">K_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:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">K\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0715em;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\">0\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":712,"meaning":3631,"symbolHtml":3632},"nominaler Zinssatz pro Jahr als Dezimalzahl, z.B. 0,05 für 5 %","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation 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style=\"height:0.6151em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">t\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":590,"meaning":3637,"symbolHtml":3638},"Anzahl der Zinsgutschriften pro Jahr","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>m\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">m\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":727,"meaning":3640,"symbolHtml":3641},"Eulersche Zahl, etwa 2,718","\u003Cspan class=\"katex\">\u003Cspan 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