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Statt mit ",[573,1121,1123,1141],{"className":1122},[576],[573,1124,1126],{"className":1125},[580],[582,1127,1128],{"xmlns":584},[586,1129,1130,1138],{},[589,1131,1132],{},[790,1133,1134,1136],{},[595,1135,794],{},[595,1137,775],{},[603,1139,1140],{"encoding":605},"q^n",[573,1142,1144],{"className":1143,"ariaHidden":611},[610],[573,1145,1147,1150],{"className":1146},[615],[573,1148],{"className":1149,"style":925},[619],[573,1151,1153,1156],{"className":1152},[624],[573,1154,794],{"className":1155,"style":932},[624,628],[573,1157,1159],{"className":1158},[633],[573,1160,1162],{"className":1161},[637],[573,1163,1165],{"className":1164},[642],[573,1166,1168],{"className":1167,"style":945},[646],[573,1169,1170,1173],{"style":948},[573,1171],{"className":1172,"style":655},[654],[573,1174,1176],{"className":1175},[659,660,661,662],[573,1177,775],{"className":1178},[624,628,662]," zu multiplizieren, teilt man durch ",[573,1181,1183,1200],{"className":1182},[576],[573,1184,1186],{"className":1185},[580],[582,1187,1188],{"xmlns":584},[586,1189,1190,1198],{},[589,1191,1192],{},[790,1193,1194,1196],{},[595,1195,794],{},[595,1197,775],{},[603,1199,1140],{"encoding":605},[573,1201,1203],{"className":1202,"ariaHidden":611},[610],[573,1204,1206,1209],{"className":1205},[615],[573,1207],{"className":1208,"style":925},[619],[573,1210,1212,1215],{"className":1211},[624],[573,1213,794],{"className":1214,"style":932},[624,628],[573,1216,1218],{"className":1217},[633],[573,1219,1221],{"className":1220},[637],[573,1222,1224],{"className":1223},[642],[573,1225,1227],{"className":1226,"style":945},[646],[573,1228,1229,1232],{"style":948},[573,1230],{"className":1231,"style":655},[654],[573,1233,1235],{"className":1234},[659,660,661,662],[573,1236,775],{"className":1237},[624,628,662],". Den Faktor ",[573,1240,1242,1264],{"className":1241},[576],[573,1243,1245],{"className":1244},[580],[582,1246,1247],{"xmlns":584},[586,1248,1249,1261],{},[589,1250,1251],{},[982,1252,1253,1255],{},[599,1254,977],{},[790,1256,1257,1259],{},[595,1258,794],{},[595,1260,775],{},[603,1262,1263],{"encoding":605},"\\frac{1}{q^n}",[573,1265,1267],{"className":1266,"ariaHidden":611},[610],[573,1268,1270,1274],{"className":1269},[615],[573,1271],{"className":1272,"style":1273},[619],"height:1.3262em;vertical-align:-0.4811em;",[573,1275,1277,1280,1373],{"className":1276},[624],[573,1278],{"className":1279},[1046,1047],[573,1281,1283],{"className":1282},[982],[573,1284,1286,1364],{"className":1285},[637,638],[573,1287,1289,1361],{"className":1288},[642],[573,1290,1293,1338,1346],{"className":1291,"style":1292},[646],"height:0.8451em;",[573,1294,1295,1298],{"style":1063},[573,1296],{"className":1297,"style":1067},[654],[573,1299,1301],{"className":1300},[659,660,661,662],[573,1302,1304],{"className":1303},[624,662],[573,1305,1307,1310],{"className":1306},[624,662],[573,1308,794],{"className":1309,"style":932},[624,628,662],[573,1311,1313],{"className":1312},[633],[573,1314,1316],{"className":1315},[637],[573,1317,1319],{"className":1318},[642],[573,1320,1323],{"className":1321,"style":1322},[646],"height:0.5935em;",[573,1324,1326,1330],{"style":1325},"top:-2.786em;margin-right:0.0714em;",[573,1327],{"className":1328,"style":1329},[654],"height:2.5em;",[573,1331,1335],{"className":1332},[659,1333,1334,662],"reset-size3","size1",[573,1336,775],{"className":1337},[624,628,662],[573,1339,1340,1343],{"style":1079},[573,1341],{"className":1342,"style":1067},[654],[573,1344],{"className":1345,"style":1087},[1086],[573,1347,1349,1352],{"style":1348},"top:-3.394em;",[573,1350],{"className":1351,"style":1067},[654],[573,1353,1355],{"className":1354},[659,660,661,662],[573,1356,1358],{"className":1357},[624,662],[573,1359,977],{"className":1360},[624,662],[573,1362,670],{"className":1363},[669],[573,1365,1367],{"className":1366},[642],[573,1368,1371],{"className":1369,"style":1370},[646],"height:0.4811em;",[573,1372],{},[573,1374],{"className":1375},[1118,1047]," nennt man ",[569,1378,552],{},".",[565,1381,1382],{},"Mit Barwerten kann man Zahlungen vergleichen, die zu verschiedenen Zeitpunkten fällig sind: Man rechnet alle auf heute um und vergleicht dann.",[560,1384,1386],{"id":1385},"beispiele","Beispiele",[565,1388,1389,1390,1420,1421,1465,1466,1509],{},"In ",[573,1391,1393,1407],{"className":1392},[576],[573,1394,1396],{"className":1395},[580],[582,1397,1398],{"xmlns":584},[586,1399,1400,1405],{},[589,1401,1402],{},[599,1403,1404],{},"5",[603,1406,1404],{"encoding":605},[573,1408,1410],{"className":1409,"ariaHidden":611},[610],[573,1411,1413,1417],{"className":1412},[615],[573,1414],{"className":1415,"style":1416},[619],"height:0.6444em;",[573,1418,1404],{"className":1419},[624]," Jahren werden ",[573,1422,1424,1446],{"className":1423},[576],[573,1425,1427],{"className":1426},[580],[582,1428,1429],{"xmlns":584},[586,1430,1431,1443],{},[589,1432,1433,1436,1440],{},[599,1434,1435],{},"10",[1437,1438,1439],"mtext",{}," ",[599,1441,1442],{},"000",[603,1444,1445],{"encoding":605},"10\\,000",[573,1447,1449],{"className":1448,"ariaHidden":611},[610],[573,1450,1452,1455,1458,1462],{"className":1451},[615],[573,1453],{"className":1454,"style":1416},[619],[573,1456,1435],{"className":1457},[624],[573,1459],{"className":1460,"style":1461},[853],"margin-right:0.1667em;",[573,1463,1442],{"className":1464},[624]," € fällig. Bei ",[573,1467,1469,1490],{"className":1468},[576],[573,1470,1472],{"className":1471},[580],[582,1473,1474],{"xmlns":584},[586,1475,1476,1487],{},[589,1477,1478,1481,1483],{},[599,1479,1480],{},"4",[1437,1482,1439],{},[595,1484,1486],{"mathvariant":1485},"normal","%",[603,1488,1489],{"encoding":605},"4\\,\\%",[573,1491,1493],{"className":1492,"ariaHidden":611},[610],[573,1494,1496,1500,1503,1506],{"className":1495},[615],[573,1497],{"className":1498,"style":1499},[619],"height:0.8056em;vertical-align:-0.0556em;",[573,1501,1480],{"className":1502},[624],[573,1504],{"className":1505,"style":1461},[853],[573,1507,1486],{"className":1508},[624]," Zinsen ist ihr Barwert",[573,1511,1514],{"className":1512},[1513],"katex-display",[573,1515,1517,1566],{"className":1516},[576],[573,1518,1520],{"className":1519},[580],[582,1521,1523],{"xmlns":584,"display":1522},"block",[586,1524,1525,1563],{},[589,1526,1527,1533,1535,1552,1555,1558,1560],{},[592,1528,1529,1531],{},[595,1530,597],{},[599,1532,601],{},[777,1534,779],{},[982,1536,1537,1545],{},[589,1538,1539,1541,1543],{},[599,1540,1435],{},[1437,1542,1439],{},[599,1544,1442],{},[790,1546,1547,1550],{},[599,1548,1549],{},"1,04",[599,1551,1404],{},[777,1553,1554],{},"≈",[599,1556,1557],{},"8219,27",[1437,1559,1439],{},[1437,1561,1562],{},"Euro",[603,1564,1565],{"encoding":605},"K_0 = \\frac{10\\,000}{1{,}04^5} \\approx 8219{,}27\\,\\text{Euro}",[573,1567,1569,1624,1754],{"className":1568,"ariaHidden":611},[610],[573,1570,1572,1575,1615,1618,1621],{"className":1571},[615],[573,1573],{"className":1574,"style":620},[619],[573,1576,1578,1581],{"className":1577},[624],[573,1579,597],{"className":1580,"style":629},[624,628],[573,1582,1584],{"className":1583},[633],[573,1585,1587,1607],{"className":1586},[637,638],[573,1588,1590,1604],{"className":1589},[642],[573,1591,1593],{"className":1592,"style":647},[646],[573,1594,1595,1598],{"style":650},[573,1596],{"className":1597,"style":655},[654],[573,1599,1601],{"className":1600},[659,660,661,662],[573,1602,601],{"className":1603},[624,662],[573,1605,670],{"className":1606},[669],[573,1608,1610],{"className":1609},[642],[573,1611,1613],{"className":1612,"style":677},[646],[573,1614],{},[573,1616],{"className":1617,"style":854},[853],[573,1619,779],{"className":1620},[858],[573,1622],{"className":1623,"style":854},[853],[573,1625,1627,1631,1745,1748,1751],{"className":1626},[615],[573,1628],{"className":1629,"style":1630},[619],"height:2.2019em;vertical-align:-0.8804em;",[573,1632,1634,1637,1742],{"className":1633},[624],[573,1635],{"className":1636},[1046,1047],[573,1638,1640],{"className":1639},[982],[573,1641,1643,1733],{"className":1642},[637,638],[573,1644,1646,1730],{"className":1645},[642],[573,1647,1650,1704,1712],{"className":1648,"style":1649},[646],"height:1.3214em;",[573,1651,1653,1656],{"style":1652},"top:-2.314em;",[573,1654],{"className":1655,"style":1067},[654],[573,1657,1659,1662,1670,1673],{"className":1658},[624],[573,1660,977],{"className":1661},[624],[573,1663,1665],{"className":1664},[624],[573,1666,1669],{"className":1667},[1668],"mpunct",",",[573,1671,601],{"className":1672},[624],[573,1674,1676,1679],{"className":1675},[624],[573,1677,1480],{"className":1678},[624],[573,1680,1682],{"className":1681},[633],[573,1683,1685],{"className":1684},[637],[573,1686,1688],{"className":1687},[642],[573,1689,1692],{"className":1690,"style":1691},[646],"height:0.7401em;",[573,1693,1695,1698],{"style":1694},"top:-2.989em;margin-right:0.05em;",[573,1696],{"className":1697,"style":655},[654],[573,1699,1701],{"className":1700},[659,660,661,662],[573,1702,1404],{"className":1703},[624,662],[573,1705,1706,1709],{"style":1079},[573,1707],{"className":1708,"style":1067},[654],[573,1710],{"className":1711,"style":1087},[1086],[573,1713,1715,1718],{"style":1714},"top:-3.677em;",[573,1716],{"className":1717,"style":1067},[654],[573,1719,1721,1724,1727],{"className":1720},[624],[573,1722,1435],{"className":1723},[624],[573,1725],{"className":1726,"style":1461},[853],[573,1728,1442],{"className":1729},[624],[573,1731,670],{"className":1732},[669],[573,1734,1736],{"className":1735},[642],[573,1737,1740],{"className":1738,"style":1739},[646],"height:0.8804em;",[573,1741],{},[573,1743],{"className":1744},[1118,1047],[573,1746],{"className":1747,"style":854},[853],[573,1749,1554],{"className":1750},[858],[573,1752],{"className":1753,"style":854},[853],[573,1755,1757,1761,1765,1771,1775,1778],{"className":1756},[615],[573,1758],{"className":1759,"style":1760},[619],"height:0.8778em;vertical-align:-0.1944em;",[573,1762,1764],{"className":1763},[624],"8219",[573,1766,1768],{"className":1767},[624],[573,1769,1669],{"className":1770},[1668],[573,1772,1774],{"className":1773},[624],"27",[573,1776],{"className":1777,"style":1461},[853],[573,1779,1782],{"className":1780},[624,1781],"text",[573,1783,1562],{"className":1784},[624],[565,1786,1787,1788,1379],{},"Der Abzinsungsfaktor ist ",[573,1789,1791,1818],{"className":1790},[576],[573,1792,1794],{"className":1793},[580],[582,1795,1796],{"xmlns":584},[586,1797,1798,1815],{},[589,1799,1800,1810,1812],{},[982,1801,1802,1804],{},[599,1803,977],{},[790,1805,1806,1808],{},[599,1807,1549],{},[599,1809,1404],{},[777,1811,1554],{},[599,1813,1814],{},"0,8219",[603,1816,1817],{"encoding":605},"\\frac{1}{1{,}04^5} \\approx 0{,}8219",[573,1819,1821,1943],{"className":1820,"ariaHidden":611},[610],[573,1822,1824,1827,1934,1937,1940],{"className":1823},[615],[573,1825],{"className":1826,"style":1273},[619],[573,1828,1830,1833,1931],{"className":1829},[624],[573,1831],{"className":1832},[1046,1047],[573,1834,1836],{"className":1835},[982],[573,1837,1839,1923],{"className":1838},[637,638],[573,1840,1842,1920],{"className":1841},[642],[573,1843,1845,1898,1906],{"className":1844,"style":1292},[646],[573,1846,1847,1850],{"style":1063},[573,1848],{"className":1849,"style":1067},[654],[573,1851,1853],{"className":1852},[659,660,661,662],[573,1854,1856,1859,1865,1868],{"className":1855},[624,662],[573,1857,977],{"className":1858},[624,662],[573,1860,1862],{"className":1861},[624,662],[573,1863,1669],{"className":1864},[1668,662],[573,1866,601],{"className":1867},[624,662],[573,1869,1871,1874],{"className":1870},[624,662],[573,1872,1480],{"className":1873},[624,662],[573,1875,1877],{"className":1876},[633],[573,1878,1880],{"className":1879},[637],[573,1881,1883],{"className":1882},[642],[573,1884,1887],{"className":1885,"style":1886},[646],"height:0.7463em;",[573,1888,1889,1892],{"style":1325},[573,1890],{"className":1891,"style":1329},[654],[573,1893,1895],{"className":1894},[659,1333,1334,662],[573,1896,1404],{"className":1897},[624,662],[573,1899,1900,1903],{"style":1079},[573,1901],{"className":1902,"style":1067},[654],[573,1904],{"className":1905,"style":1087},[1086],[573,1907,1908,1911],{"style":1348},[573,1909],{"className":1910,"style":1067},[654],[573,1912,1914],{"className":1913},[659,660,661,662],[573,1915,1917],{"className":1916},[624,662],[573,1918,977],{"className":1919},[624,662],[573,1921,670],{"className":1922},[669],[573,1924,1926],{"className":1925},[642],[573,1927,1929],{"className":1928,"style":1370},[646],[573,1930],{},[573,1932],{"className":1933},[1118,1047],[573,1935],{"className":1936,"style":854},[853],[573,1938,1554],{"className":1939},[858],[573,1941],{"className":1942,"style":854},[853],[573,1944,1946,1950,1953,1959],{"className":1945},[615],[573,1947],{"className":1948,"style":1949},[619],"height:0.8389em;vertical-align:-0.1944em;",[573,1951,601],{"className":1952},[624],[573,1954,1956],{"className":1955},[624],[573,1957,1669],{"className":1958},[1668],[573,1960,1764],{"className":1961},[624],[565,1963,1964,1965,1994,1995,2024,2025,2054,2055,2094],{},"Eine Person kann heute ",[573,1966,1968,1982],{"className":1967},[576],[573,1969,1971],{"className":1970},[580],[582,1972,1973],{"xmlns":584},[586,1974,1975,1980],{},[589,1976,1977],{},[599,1978,1979],{},"5000",[603,1981,1979],{"encoding":605},[573,1983,1985],{"className":1984,"ariaHidden":611},[610],[573,1986,1988,1991],{"className":1987},[615],[573,1989],{"className":1990,"style":1416},[619],[573,1992,1979],{"className":1993},[624]," € bekommen oder in ",[573,1996,1998,2012],{"className":1997},[576],[573,1999,2001],{"className":2000},[580],[582,2002,2003],{"xmlns":584},[586,2004,2005,2010],{},[589,2006,2007],{},[599,2008,2009],{},"3",[603,2011,2009],{"encoding":605},[573,2013,2015],{"className":2014,"ariaHidden":611},[610],[573,2016,2018,2021],{"className":2017},[615],[573,2019],{"className":2020,"style":1416},[619],[573,2022,2009],{"className":2023},[624]," Jahren ",[573,2026,2028,2042],{"className":2027},[576],[573,2029,2031],{"className":2030},[580],[582,2032,2033],{"xmlns":584},[586,2034,2035,2040],{},[589,2036,2037],{},[599,2038,2039],{},"5500",[603,2041,2039],{"encoding":605},[573,2043,2045],{"className":2044,"ariaHidden":611},[610],[573,2046,2048,2051],{"className":2047},[615],[573,2049],{"className":2050,"style":1416},[619],[573,2052,2039],{"className":2053},[624]," €. Der Zinssatz für eine sichere Anlage ist ",[573,2056,2058,2076],{"className":2057},[576],[573,2059,2061],{"className":2060},[580],[582,2062,2063],{"xmlns":584},[586,2064,2065,2073],{},[589,2066,2067,2069,2071],{},[599,2068,2009],{},[1437,2070,1439],{},[595,2072,1486],{"mathvariant":1485},[603,2074,2075],{"encoding":605},"3\\,\\%",[573,2077,2079],{"className":2078,"ariaHidden":611},[610],[573,2080,2082,2085,2088,2091],{"className":2081},[615],[573,2083],{"className":2084,"style":1499},[619],[573,2086,2009],{"className":2087},[624],[573,2089],{"className":2090,"style":1461},[853],[573,2092,1486],{"className":2093},[624],". Barwert des späteren Angebots:",[573,2096,2098],{"className":2097},[1513],[573,2099,2101,2141],{"className":2100},[576],[573,2102,2104],{"className":2103},[580],[582,2105,2106],{"xmlns":584,"display":1522},[586,2107,2108,2138],{},[589,2109,2110,2116,2118,2129,2131,2134,2136],{},[592,2111,2112,2114],{},[595,2113,597],{},[599,2115,601],{},[777,2117,779],{},[982,2119,2120,2122],{},[599,2121,2039],{},[790,2123,2124,2127],{},[599,2125,2126],{},"1,03",[599,2128,2009],{},[777,2130,1554],{},[599,2132,2133],{},"5033,28",[1437,2135,1439],{},[1437,2137,1562],{},[603,2139,2140],{"encoding":605},"K_0 = \\frac{5500}{1{,}03^3} \\approx 5033{,}28\\,\\text{Euro}",[573,2142,2144,2199,2314],{"className":2143,"ariaHidden":611},[610],[573,2145,2147,2150,2190,2193,2196],{"className":2146},[615],[573,2148],{"className":2149,"style":620},[619],[573,2151,2153,2156],{"className":2152},[624],[573,2154,597],{"className":2155,"style":629},[624,628],[573,2157,2159],{"className":2158},[633],[573,2160,2162,2182],{"className":2161},[637,638],[573,2163,2165,2179],{"className":2164},[642],[573,2166,2168],{"className":2167,"style":647},[646],[573,2169,2170,2173],{"style":650},[573,2171],{"className":2172,"style":655},[654],[573,2174,2176],{"className":2175},[659,660,661,662],[573,2177,601],{"className":2178},[624,662],[573,2180,670],{"className":2181},[669],[573,2183,2185],{"className":2184},[642],[573,2186,2188],{"className":2187,"style":677},[646],[573,2189],{},[573,2191],{"className":2192,"style":854},[853],[573,2194,779],{"className":2195},[858],[573,2197],{"className":2198,"style":854},[853],[573,2200,2202,2205,2305,2308,2311],{"className":2201},[615],[573,2203],{"className":2204,"style":1630},[619],[573,2206,2208,2211,2302],{"className":2207},[624],[573,2209],{"className":2210},[1046,1047],[573,2212,2214],{"className":2213},[982],[573,2215,2217,2294],{"className":2216},[637,638],[573,2218,2220,2291],{"className":2219},[642],[573,2221,2223,2272,2280],{"className":2222,"style":1649},[646],[573,2224,2225,2228],{"style":1652},[573,2226],{"className":2227,"style":1067},[654],[573,2229,2231,2234,2240,2243],{"className":2230},[624],[573,2232,977],{"className":2233},[624],[573,2235,2237],{"className":2236},[624],[573,2238,1669],{"className":2239},[1668],[573,2241,601],{"className":2242},[624],[573,2244,2246,2249],{"className":2245},[624],[573,2247,2009],{"className":2248},[624],[573,2250,2252],{"className":2251},[633],[573,2253,2255],{"className":2254},[637],[573,2256,2258],{"className":2257},[642],[573,2259,2261],{"className":2260,"style":1691},[646],[573,2262,2263,2266],{"style":1694},[573,2264],{"className":2265,"style":655},[654],[573,2267,2269],{"className":2268},[659,660,661,662],[573,2270,2009],{"className":2271},[624,662],[573,2273,2274,2277],{"style":1079},[573,2275],{"className":2276,"style":1067},[654],[573,2278],{"className":2279,"style":1087},[1086],[573,2281,2282,2285],{"style":1714},[573,2283],{"className":2284,"style":1067},[654],[573,2286,2288],{"className":2287},[624],[573,2289,2039],{"className":2290},[624],[573,2292,670],{"className":2293},[669],[573,2295,2297],{"className":2296},[642],[573,2298,2300],{"className":2299,"style":1739},[646],[573,2301],{},[573,2303],{"className":2304},[1118,1047],[573,2306],{"className":2307,"style":854},[853],[573,2309,1554],{"className":2310},[858],[573,2312],{"className":2313,"style":854},[853],[573,2315,2317,2320,2324,2330,2334,2337],{"className":2316},[615],[573,2318],{"className":2319,"style":1760},[619],[573,2321,2323],{"className":2322},[624],"5033",[573,2325,2327],{"className":2326},[624],[573,2328,1669],{"className":2329},[1668],[573,2331,2333],{"className":2332},[624],"28",[573,2335],{"className":2336,"style":1461},[853],[573,2338,2340],{"className":2339},[624,1781],[573,2341,1562],{"className":2342},[624],[565,2344,2345,2346,2374,2375,2403,2404,2432,2433,2562],{},"Das ist mehr als ",[573,2347,2349,2362],{"className":2348},[576],[573,2350,2352],{"className":2351},[580],[582,2353,2354],{"xmlns":584},[586,2355,2356,2360],{},[589,2357,2358],{},[599,2359,1979],{},[603,2361,1979],{"encoding":605},[573,2363,2365],{"className":2364,"ariaHidden":611},[610],[573,2366,2368,2371],{"className":2367},[615],[573,2369],{"className":2370,"style":1416},[619],[573,2372,1979],{"className":2373},[624]," €, das spätere Angebot ist also etwas besser. Gegenprobe: ",[573,2376,2378,2391],{"className":2377},[576],[573,2379,2381],{"className":2380},[580],[582,2382,2383],{"xmlns":584},[586,2384,2385,2389],{},[589,2386,2387],{},[599,2388,1979],{},[603,2390,1979],{"encoding":605},[573,2392,2394],{"className":2393,"ariaHidden":611},[610],[573,2395,2397,2400],{"className":2396},[615],[573,2398],{"className":2399,"style":1416},[619],[573,2401,1979],{"className":2402},[624]," € heute angelegt ergeben nach ",[573,2405,2407,2420],{"className":2406},[576],[573,2408,2410],{"className":2409},[580],[582,2411,2412],{"xmlns":584},[586,2413,2414,2418],{},[589,2415,2416],{},[599,2417,2009],{},[603,2419,2009],{"encoding":605},[573,2421,2423],{"className":2422,"ariaHidden":611},[610],[573,2424,2426,2429],{"className":2425},[615],[573,2427],{"className":2428,"style":1416},[619],[573,2430,2009],{"className":2431},[624]," Jahren nur ",[573,2434,2436,2463],{"className":2435},[576],[573,2437,2439],{"className":2438},[580],[582,2440,2441],{"xmlns":584},[586,2442,2443,2460],{},[589,2444,2445,2447,2449,2455,2457],{},[599,2446,1979],{},[777,2448,788],{},[790,2450,2451,2453],{},[599,2452,2126],{},[599,2454,2009],{},[777,2456,1554],{},[599,2458,2459],{},"5463,64",[603,2461,2462],{"encoding":605},"5000 \\cdot 1{,}03^3 \\approx 5463{,}64",[573,2464,2466,2484,2542],{"className":2465,"ariaHidden":611},[610],[573,2467,2469,2472,2475,2478,2481],{"className":2468},[615],[573,2470],{"className":2471,"style":1416},[619],[573,2473,1979],{"className":2474},[624],[573,2476],{"className":2477,"style":911},[853],[573,2479,788],{"className":2480},[915],[573,2482],{"className":2483,"style":911},[853],[573,2485,2487,2491,2494,2500,2503,2533,2536,2539],{"className":2486},[615],[573,2488],{"className":2489,"style":2490},[619],"height:1.0085em;vertical-align:-0.1944em;",[573,2492,977],{"className":2493},[624],[573,2495,2497],{"className":2496},[624],[573,2498,1669],{"className":2499},[1668],[573,2501,601],{"className":2502},[624],[573,2504,2506,2509],{"className":2505},[624],[573,2507,2009],{"className":2508},[624],[573,2510,2512],{"className":2511},[633],[573,2513,2515],{"className":2514},[637],[573,2516,2518],{"className":2517},[642],[573,2519,2522],{"className":2520,"style":2521},[646],"height:0.8141em;",[573,2523,2524,2527],{"style":948},[573,2525],{"className":2526,"style":655},[654],[573,2528,2530],{"className":2529},[659,660,661,662],[573,2531,2009],{"className":2532},[624,662],[573,2534],{"className":2535,"style":854},[853],[573,2537,1554],{"className":2538},[858],[573,2540],{"className":2541,"style":854},[853],[573,2543,2545,2548,2552,2558],{"className":2544},[615],[573,2546],{"className":2547,"style":1949},[619],[573,2549,2551],{"className":2550},[624],"5463",[573,2553,2555],{"className":2554},[624],[573,2556,1669],{"className":2557},[1668],[573,2559,2561],{"className":2560},[624],"64"," €.",[560,2564,2566],{"id":2565},"typische-fehler","Typische Fehler",[2568,2569,2570,2687,2963],"ul",{},[2571,2572,2573,2574,2632,2633,2686],"li",{},"Mit ",[573,2575,2577,2594],{"className":2576},[576],[573,2578,2580],{"className":2579},[580],[582,2581,2582],{"xmlns":584},[586,2583,2584,2592],{},[589,2585,2586],{},[790,2587,2588,2590],{},[595,2589,794],{},[595,2591,775],{},[603,2593,1140],{"encoding":605},[573,2595,2597],{"className":2596,"ariaHidden":611},[610],[573,2598,2600,2603],{"className":2599},[615],[573,2601],{"className":2602,"style":925},[619],[573,2604,2606,2609],{"className":2605},[624],[573,2607,794],{"className":2608,"style":932},[624,628],[573,2610,2612],{"className":2611},[633],[573,2613,2615],{"className":2614},[637],[573,2616,2618],{"className":2617},[642],[573,2619,2621],{"className":2620,"style":945},[646],[573,2622,2623,2626],{"style":948},[573,2624],{"className":2625,"style":655},[654],[573,2627,2629],{"className":2628},[659,660,661,662],[573,2630,775],{"className":2631},[624,628,662]," multiplizieren statt dividieren. Der Barwert ist immer kleiner als der spätere Betrag, solange ",[573,2634,2636,2655],{"className":2635},[576],[573,2637,2639],{"className":2638},[580],[582,2640,2641],{"xmlns":584},[586,2642,2643,2652],{},[589,2644,2645,2647,2650],{},[595,2646,565],{},[777,2648,2649],{},">",[599,2651,601],{},[603,2653,2654],{"encoding":605},"p > 0",[573,2656,2658,2677],{"className":2657,"ariaHidden":611},[610],[573,2659,2661,2665,2668,2671,2674],{"className":2660},[615],[573,2662],{"className":2663,"style":2664},[619],"height:0.7335em;vertical-align:-0.1944em;",[573,2666,565],{"className":2667},[624,628],[573,2669],{"className":2670,"style":854},[853],[573,2672,2649],{"className":2673},[858],[573,2675],{"className":2676,"style":854},[853],[573,2678,2680,2683],{"className":2679},[615],[573,2681],{"className":2682,"style":1416},[619],[573,2684,601],{"className":2685},[624]," ist.",[2571,2688,2689,2690,2741,2742,2862,2863,2901,2902,1379],{},"Den Zinssatz als ",[573,2691,2693,2711],{"className":2692},[576],[573,2694,2696],{"className":2695},[580],[582,2697,2698],{"xmlns":584},[586,2699,2700,2708],{},[589,2701,2702,2704,2706],{},[599,2703,977],{},[777,2705,980],{},[595,2707,565],{},[603,2709,2710],{"encoding":605},"1 + p",[573,2712,2714,2732],{"className":2713,"ariaHidden":611},[610],[573,2715,2717,2720,2723,2726,2729],{"className":2716},[615],[573,2718],{"className":2719,"style":1020},[619],[573,2721,977],{"className":2722},[624],[573,2724],{"className":2725,"style":911},[853],[573,2727,980],{"className":2728},[915],[573,2730],{"className":2731,"style":911},[853],[573,2733,2735,2738],{"className":2734},[615],[573,2736],{"className":2737,"style":1001},[619],[573,2739,565],{"className":2740},[624,628]," statt ",[573,2743,2745,2767],{"className":2744},[576],[573,2746,2748],{"className":2747},[580],[582,2749,2750],{"xmlns":584},[586,2751,2752,2764],{},[589,2753,2754,2756,2758],{},[599,2755,977],{},[777,2757,980],{},[982,2759,2760,2762],{},[595,2761,565],{},[599,2763,988],{},[603,2765,2766],{"encoding":605},"1 + \\frac{p}{100}",[573,2768,2770,2788],{"className":2769,"ariaHidden":611},[610],[573,2771,2773,2776,2779,2782,2785],{"className":2772},[615],[573,2774],{"className":2775,"style":1020},[619],[573,2777,977],{"className":2778},[624],[573,2780],{"className":2781,"style":911},[853],[573,2783,980],{"className":2784},[915],[573,2786],{"className":2787,"style":911},[853],[573,2789,2791,2794],{"className":2790},[615],[573,2792],{"className":2793,"style":1039},[619],[573,2795,2797,2800,2859],{"className":2796},[624],[573,2798],{"className":2799},[1046,1047],[573,2801,2803],{"className":2802},[982],[573,2804,2806,2851],{"className":2805},[637,638],[573,2807,2809,2848],{"className":2808},[642],[573,2810,2812,2826,2834],{"className":2811,"style":1060},[646],[573,2813,2814,2817],{"style":1063},[573,2815],{"className":2816,"style":1067},[654],[573,2818,2820],{"className":2819},[659,660,661,662],[573,2821,2823],{"className":2822},[624,662],[573,2824,988],{"className":2825},[624,662],[573,2827,2828,2831],{"style":1079},[573,2829],{"className":2830,"style":1067},[654],[573,2832],{"className":2833,"style":1087},[1086],[573,2835,2836,2839],{"style":1090},[573,2837],{"className":2838,"style":1067},[654],[573,2840,2842],{"className":2841},[659,660,661,662],[573,2843,2845],{"className":2844},[624,662],[573,2846,565],{"className":2847},[624,628,662],[573,2849,670],{"className":2850},[669],[573,2852,2854],{"className":2853},[642],[573,2855,2857],{"className":2856,"style":1112},[646],[573,2858],{},[573,2860],{"className":2861},[1118,1047]," einsetzen: Bei ",[573,2864,2866,2883],{"className":2865},[576],[573,2867,2869],{"className":2868},[580],[582,2870,2871],{"xmlns":584},[586,2872,2873,2881],{},[589,2874,2875,2877,2879],{},[599,2876,1480],{},[1437,2878,1439],{},[595,2880,1486],{"mathvariant":1485},[603,2882,1489],{"encoding":605},[573,2884,2886],{"className":2885,"ariaHidden":611},[610],[573,2887,2889,2892,2895,2898],{"className":2888},[615],[573,2890],{"className":2891,"style":1499},[619],[573,2893,1480],{"className":2894},[624],[573,2896],{"className":2897,"style":1461},[853],[573,2899,1486],{"className":2900},[624]," ist ",[573,2903,2905,2923],{"className":2904},[576],[573,2906,2908],{"className":2907},[580],[582,2909,2910],{"xmlns":584},[586,2911,2912,2920],{},[589,2913,2914,2916,2918],{},[595,2915,794],{},[777,2917,779],{},[599,2919,1549],{},[603,2921,2922],{"encoding":605},"q = 1{,}04",[573,2924,2926,2944],{"className":2925,"ariaHidden":611},[610],[573,2927,2929,2932,2935,2938,2941],{"className":2928},[615],[573,2930],{"className":2931,"style":1001},[619],[573,2933,794],{"className":2934,"style":932},[624,628],[573,2936],{"className":2937,"style":854},[853],[573,2939,779],{"className":2940},[858],[573,2942],{"className":2943,"style":854},[853],[573,2945,2947,2950,2953,2959],{"className":2946},[615],[573,2948],{"className":2949,"style":1949},[619],[573,2951,977],{"className":2952},[624],[573,2954,2956],{"className":2955},[624],[573,2957,1669],{"className":2958},[1668],[573,2960,2962],{"className":2961},[624],"04",[2571,2964,2965,2966,3051],{},"Einfache Zinsen abziehen, also ",[573,2967,2969,2997],{"className":2968},[576],[573,2970,2972],{"className":2971},[580],[582,2973,2974],{"xmlns":584},[586,2975,2976,2994],{},[589,2977,2978,2980,2982,2984,2987,2989,2991],{},[599,2979,1435],{},[1437,2981,1439],{},[599,2983,1442],{},[777,2985,2986],{},"−",[599,2988,1404],{},[777,2990,788],{},[599,2992,2993],{},"400",[603,2995,2996],{"encoding":605},"10\\,000 - 5 \\cdot 400",[573,2998,3000,3024,3042],{"className":2999,"ariaHidden":611},[610],[573,3001,3003,3006,3009,3012,3015,3018,3021],{"className":3002},[615],[573,3004],{"className":3005,"style":1020},[619],[573,3007,1435],{"className":3008},[624],[573,3010],{"className":3011,"style":1461},[853],[573,3013,1442],{"className":3014},[624],[573,3016],{"className":3017,"style":911},[853],[573,3019,2986],{"className":3020},[915],[573,3022],{"className":3023,"style":911},[853],[573,3025,3027,3030,3033,3036,3039],{"className":3026},[615],[573,3028],{"className":3029,"style":1416},[619],[573,3031,1404],{"className":3032},[624],[573,3034],{"className":3035,"style":911},[853],[573,3037,788],{"className":3038},[915],[573,3040],{"className":3041,"style":911},[853],[573,3043,3045,3048],{"className":3044},[615],[573,3046],{"className":3047,"style":1416},[619],[573,3049,2993],{"className":3050},[624]," rechnen. Abzinsen berücksichtigt den Zinseszins.",{"title":3053,"searchDepth":3054,"depth":3054,"links":3055},"",2,[3056,3057,3058],{"id":562,"depth":3054,"text":563},{"id":1385,"depth":3054,"text":1386},{"id":2565,"depth":3054,"text":2566},[3060,3062,3065,3068,3071],{"lhs":3061,"rhs":597},"(K * (1 + p\u002F100)^n) \u002F (1 + p\u002F100)^n",{"lhs":3063,"rhs":3064},"round(10000 \u002F 1.04^5, 2)","8219.27",{"lhs":3066,"rhs":3067},"round(1 \u002F 1.04^5, 4)","0.8219",{"lhs":3069,"rhs":3070},"round(5500 \u002F 1.03^3, 2)","5033.28",{"lhs":3072,"rhs":3073},"round(5000 * 1.03^3, 2)","5463.64","p > -100,\\ n \\geq 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>100\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p > -100,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7335em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">−\u003C\u002Fspan>\u003Cspan class=\"mord\">100\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\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\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","present-value","K_0 = \\frac{K_n}{\\left(1 + \\frac{p}{100}\\right)^n}","\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>K\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmsub>\u003Cmi>K\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmsup>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>+\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>100\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">K_0 = \\frac{K_n}{\\left(1 + \\frac{p}{100}\\right)^n}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">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:0.2778em;\">\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:2.5046em;vertical-align:-1.1443em;\">\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:1.3603em;\">\u003Cspan style=\"top:-2.2057em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"minner\">\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">(\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:0.7475em;\">\u003Cspan style=\"top:-2.655em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">100\u003C\u002Fspan>\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:-3.4461em;\">\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\">p\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:0.345em;\">\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 size1\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9043em;\">\u003Cspan style=\"top:-3.3029em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">K\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" 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nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","middle",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Farithmetic\u002Fbarwert",[],[3087,3088,3089],"compound-interest","annuity-present-value","simple-interest",{"title":548,"description":3053},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fbarwert","Der Barwert ist der heutige Wert einer späteren Zahlung; man zinst sie mit dem Zinseszins zurück.",[3094,3095,3096,3097,3098],"abzinsen","zinseszins","kapital","zinsen","finanzmathematik",[3100,3103,3107,3110],{"symbol":606,"meaning":3101,"symbolHtml":3102},"Barwert, der heutige Wert einer späteren Zahlung","\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":3104,"meaning":3105,"symbolHtml":3106},"K_n","Betrag, der nach n Jahren gezahlt wird","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>K\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">K_n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">K\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":565,"meaning":3108,"symbolHtml":3109},"Zinssatz in Prozent pro Jahr","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":775,"meaning":3111,"symbolHtml":3112},"Anzahl der Jahre bis zur Zahlung","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","6qWOQAW052-o_VWEs_-l4wF2sdE8mUueuQeczbStCt8",[3115,3118,3121],{"stem":3116,"title":3117,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fjahreszinsen","Jahreszinsen",{"stem":3119,"title":3120,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Frentenbarwert","Rentenbarwert",{"stem":3122,"title":3123,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fzinseszins","Zinseszins",1793824258959]