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Die Formel gilt für jährliche Raten am Jahresende mit einem Jahreszins.",[560,1032,1034],{"id":1033},"herleitung","Herleitung",[565,1036,1037,1038,1166,1167,1344],{},"Ohne Zahlungen wüchse die Schuld auf ",[577,1039,1041,1068],{"className":1040},[580],[577,1042,1044],{"className":1043},[584],[586,1045,1046],{"xmlns":588},[590,1047,1048,1065],{},[593,1049,1050,1056,1059],{},[691,1051,1052,1054],{},[596,1053,695],{},[697,1055,699],{},[826,1057,1058],{},"⋅",[818,1060,1061,1063],{},[596,1062,822],{},[596,1064,661],{},[600,1066,1067],{"encoding":602},"K_0 \\cdot q^n",[577,1069,1071,1128],{"className":1070,"ariaHidden":607},[606],[577,1072,1074,1077,1117,1122,1125],{"className":1073},[611],[577,1075],{"className":1076,"style":712},[615],[577,1078,1080,1083],{"className":1079},[620],[577,1081,695],{"className":1082,"style":719},[620,621],[577,1084,1086],{"className":1085},[723],[577,1087,1089,1109],{"className":1088},[727,728],[577,1090,1092,1106],{"className":1091},[732],[577,1093,1095],{"className":1094,"style":737},[736],[577,1096,1097,1100],{"style":740},[577,1098],{"className":1099,"style":745},[744],[577,1101,1103],{"className":1102},[749,750,751,752],[577,1104,699],{"className":1105},[620,752],[577,1107,760],{"className":1108},[759],[577,1110,1112],{"className":1111},[732],[577,1113,1115],{"className":1114,"style":767},[736],[577,1116],{},[577,1118],{"className":1119,"style":1121},[1120],"mspace","margin-right:0.2222em;",[577,1123,1058],{"className":1124},[938],[577,1126],{"className":1127,"style":1121},[1120],[577,1129,1131,1135],{"className":1130},[611],[577,1132],{"className":1133,"style":1134},[615],"height:0.8588em;vertical-align:-0.1944em;",[577,1136,1138,1141],{"className":1137},[620],[577,1139,822],{"className":1140,"style":906},[620,621],[577,1142,1144],{"className":1143},[723],[577,1145,1147],{"className":1146},[727],[577,1148,1150],{"className":1149},[732],[577,1151,1154],{"className":1152,"style":1153},[736],"height:0.6644em;",[577,1155,1157,1160],{"style":1156},"top:-3.063em;margin-right:0.05em;",[577,1158],{"className":1159,"style":745},[744],[577,1161,1163],{"className":1162},[749,750,751,752],[577,1164,661],{"className":1165},[620,621,752],". Die Raten wachsen wie bei einem Sparplan auf ",[577,1168,1170,1208],{"className":1169},[580],[577,1171,1173],{"className":1172},[584],[586,1174,1175],{"xmlns":588},[590,1176,1177,1205],{},[593,1178,1179,1181,1183],{},[596,1180,598],{},[826,1182,1058],{},[813,1184,1185,1197],{},[593,1186,1187,1193,1195],{},[818,1188,1189,1191],{},[596,1190,822],{},[596,1192,661],{},[826,1194,834],{},[697,1196,837],{},[593,1198,1199,1201,1203],{},[596,1200,822],{},[826,1202,834],{},[697,1204,837],{},[600,1206,1207],{"encoding":602},"A \\cdot \\frac{q^n - 1}{q - 1}",[577,1209,1211,1229],{"className":1210,"ariaHidden":607},[606],[577,1212,1214,1217,1220,1223,1226],{"className":1213},[611],[577,1215],{"className":1216,"style":616},[615],[577,1218,598],{"className":1219},[620,621],[577,1221],{"className":1222,"style":1121},[1120],[577,1224,1058],{"className":1225},[938],[577,1227],{"className":1228,"style":1121},[1120],[577,1230,1232,1236],{"className":1231},[611],[577,1233],{"className":1234,"style":1235},[615],"height:1.4442em;vertical-align:-0.4811em;",[577,1237,1239,1242,1341],{"className":1238},[620],[577,1240],{"className":1241},[872,873],[577,1243,1245],{"className":1244},[813],[577,1246,1248,1333],{"className":1247},[727,728],[577,1249,1251,1330],{"className":1250},[732],[577,1252,1255,1275,1283],{"className":1253,"style":1254},[736],"height:0.9631em;",[577,1256,1257,1260],{"style":889},[577,1258],{"className":1259,"style":893},[744],[577,1261,1263],{"className":1262},[749,750,751,752],[577,1264,1266,1269,1272],{"className":1265},[620,752],[577,1267,822],{"className":1268,"style":906},[620,621,752],[577,1270,834],{"className":1271},[938,752],[577,1273,837],{"className":1274},[620,752],[577,1276,1277,1280],{"style":944},[577,1278],{"className":1279,"style":893},[744],[577,1281],{"className":1282,"style":952},[951],[577,1284,1286,1289],{"style":1285},"top:-3.4461em;",[577,1287],{"className":1288,"style":893},[744],[577,1290,1292],{"className":1291},[749,750,751,752],[577,1293,1295,1324,1327],{"className":1294},[620,752],[577,1296,1298,1301],{"className":1297},[620,752],[577,1299,822],{"className":1300,"style":906},[620,621,752],[577,1302,1304],{"className":1303},[723],[577,1305,1307],{"className":1306},[727],[577,1308,1310],{"className":1309},[732],[577,1311,1313],{"className":1312,"style":983},[736],[577,1314,1315,1318],{"style":986},[577,1316],{"className":1317,"style":926},[744],[577,1319,1321],{"className":1320},[749,930,931,752],[577,1322,661],{"className":1323},[620,621,752],[577,1325,834],{"className":1326},[938,752],[577,1328,837],{"className":1329},[620,752],[577,1331,760],{"className":1332},[759],[577,1334,1336],{"className":1335},[732],[577,1337,1339],{"className":1338,"style":1021},[736],[577,1340],{},[577,1342],{"className":1343},[1011,873],". Am Ende soll beides gleich sein:",[577,1346,1349],{"className":1347},[1348],"katex-display",[577,1350,1352,1460],{"className":1351},[580],[577,1353,1355],{"className":1354},[584],[586,1356,1358],{"xmlns":588,"display":1357},"block",[590,1359,1360,1457],{},[593,1361,1362,1368,1370,1376,1379,1381,1383,1405,1408,1411,1413,1415,1417,1423,1425],{},[691,1363,1364,1366],{},[596,1365,695],{},[697,1367,699],{},[826,1369,1058],{},[818,1371,1372,1374],{},[596,1373,822],{},[596,1375,661],{},[826,1377,1378],{},"=",[596,1380,598],{},[826,1382,1058],{},[813,1384,1385,1397],{},[593,1386,1387,1393,1395],{},[818,1388,1389,1391],{},[596,1390,822],{},[596,1392,661],{},[826,1394,834],{},[697,1396,837],{},[593,1398,1399,1401,1403],{},[596,1400,822],{},[826,1402,834],{},[697,1404,837],{},[1120,1406],{"width":1407},"1em",[826,1409,1410],{},"⇒",[1120,1412],{"width":1407},[596,1414,598],{},[826,1416,1378],{},[691,1418,1419,1421],{},[596,1420,695],{},[697,1422,699],{},[826,1424,1058],{},[813,1426,1427,1445],{},[593,1428,1429,1435,1437,1439,1441,1443],{},[818,1430,1431,1433],{},[596,1432,822],{},[596,1434,661],{},[826,1436,829],{"stretchy":828},[596,1438,822],{},[826,1440,834],{},[697,1442,837],{},[826,1444,840],{"stretchy":828},[593,1446,1447,1453,1455],{},[818,1448,1449,1451],{},[596,1450,822],{},[596,1452,661],{},[826,1454,834],{},[697,1456,837],{},[600,1458,1459],{"encoding":602},"K_0 \\cdot q^n = A \\cdot \\frac{q^n - 1}{q - 1} \\quad\\Rightarrow\\quad A = K_0 \\cdot \\frac{q^n (q - 1)}{q^n - 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Kredit über ",[577,1962,1964,1986],{"className":1963},[580],[577,1965,1967],{"className":1966},[584],[586,1968,1969],{"xmlns":588},[590,1970,1971,1983],{},[593,1972,1973,1976,1980],{},[697,1974,1975],{},"10",[1977,1978,1979],"mtext",{}," ",[697,1981,1982],{},"000",[600,1984,1985],{"encoding":602},"10\\,000",[577,1987,1989],{"className":1988,"ariaHidden":607},[606],[577,1990,1992,1996,1999,2003],{"className":1991},[611],[577,1993],{"className":1994,"style":1995},[615],"height:0.6444em;",[577,1997,1975],{"className":1998},[620],[577,2000],{"className":2001,"style":2002},[1120],"margin-right:0.1667em;",[577,2004,1982],{"className":2005},[620]," € soll bei 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werden:",[577,2081,2083],{"className":2082},[1348],[577,2084,2086,2149],{"className":2085},[580],[577,2087,2089],{"className":2088},[584],[586,2090,2091],{"xmlns":588,"display":1357},[590,2092,2093,2146],{},[593,2094,2095,2097,2099,2101,2103,2105,2107,2135,2138,2141,2143],{},[596,2096,598],{},[826,2098,1378],{},[697,2100,1975],{},[1977,2102,1979],{},[697,2104,1982],{},[826,2106,1058],{},[813,2108,2109,2123],{},[593,2110,2111,2118,2120],{},[818,2112,2113,2116],{},[697,2114,2115],{},"1,05",[697,2117,2021],{},[826,2119,1058],{},[697,2121,2122],{},"0,05",[593,2124,2125,2131,2133],{},[818,2126,2127,2129],{},[697,2128,2115],{},[697,2130,2021],{},[826,2132,834],{},[697,2134,837],{},[826,2136,2137],{},"≈",[697,2139,2140],{},"2309,75",[1977,2142,1979],{},[1977,2144,2145],{},"Euro",[600,2147,2148],{"encoding":602},"A = 10\\,000 \\cdot \\frac{1{,}05^5 \\cdot 0{,}05}{1{,}05^5 - 1} \\approx 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zahlt man ",[577,2422,2424,2452],{"className":2423},[580],[577,2425,2427],{"className":2426},[584],[586,2428,2429],{"xmlns":588},[590,2430,2431,2449],{},[593,2432,2433,2435,2437,2439,2441,2444,2446],{},[697,2434,2021],{},[826,2436,1058],{},[596,2438,598],{},[826,2440,2137],{},[697,2442,2443],{},"11",[1977,2445,1979],{},[697,2447,2448],{},"548,74",[600,2450,2451],{"encoding":602},"5 \\cdot A \\approx 11\\,548{,}74",[577,2453,2455,2473,2491],{"className":2454,"ariaHidden":607},[606],[577,2456,2458,2461,2464,2467,2470],{"className":2457},[611],[577,2459],{"className":2460,"style":1995},[615],[577,2462,2021],{"className":2463},[620],[577,2465],{"className":2466,"style":1121},[1120],[577,2468,1058],{"className":2469},[938],[577,2471],{"className":2472,"style":1121},[1120],[577,2474,2476,2479,2482,2485,2488],{"className":2475},[611],[577,2477],{"className":2478,"style":616},[615],[577,2480,598],{"className":2481},[620,621],[577,2483],{"className":2484,"style":1559},[1120],[577,2486,2137],{"className":2487},[1563],[577,2489],{"className":2490,"style":1559},[1120],[577,2492,2494,2498,2501,2504,2508,2514],{"className":2493},[611],[577,2495],{"className":2496,"style":2497},[615],"height:0.8389em;vertical-align:-0.1944em;",[577,2499,2443],{"className":2500},[620],[577,2502],{"className":2503,"style":2002},[1120],[577,2505,2507],{"className":2506},[620],"548",[577,2509,2511],{"className":2510},[620],[577,2512,2238],{"className":2513},[2237],[577,2515,2517],{"className":2516},[620],"74"," €, davon sind ",[577,2520,2522,2537],{"className":2521},[580],[577,2523,2525],{"className":2524},[584],[586,2526,2527],{"xmlns":588},[590,2528,2529,2534],{},[593,2530,2531],{},[697,2532,2533],{},"1548,74",[600,2535,2536],{"encoding":602},"1548{,}74",[577,2538,2540],{"className":2539,"ariaHidden":607},[606],[577,2541,2543,2546,2550,2556],{"className":2542},[611],[577,2544],{"className":2545,"style":2497},[615],[577,2547,2549],{"className":2548},[620],"1548",[577,2551,2553],{"className":2552},[620],[577,2554,2238],{"className":2555},[2237],[577,2557,2517],{"className":2558},[620]," € Zinsen.",[565,2561,2562,2563,2603,2604,2655,2656,2685],{},"Eine Baufinanzierung über ",[577,2564,2566,2585],{"className":2565},[580],[577,2567,2569],{"className":2568},[584],[586,2570,2571],{"xmlns":588},[590,2572,2573,2582],{},[593,2574,2575,2578,2580],{},[697,2576,2577],{},"200",[1977,2579,1979],{},[697,2581,1982],{},[600,2583,2584],{"encoding":602},"200\\,000",[577,2586,2588],{"className":2587,"ariaHidden":607},[606],[577,2589,2591,2594,2597,2600],{"className":2590},[611],[577,2592],{"className":2593,"style":1995},[615],[577,2595,2577],{"className":2596},[620],[577,2598],{"className":2599,"style":2002},[1120],[577,2601,1982],{"className":2602},[620]," € bei ",[577,2605,2607,2626],{"className":2606},[580],[577,2608,2610],{"className":2609},[584],[586,2611,2612],{"xmlns":588},[590,2613,2614,2623],{},[593,2615,2616,2619,2621],{},[697,2617,2618],{},"3,5",[1977,2620,1979],{},[596,2622,2027],{"mathvariant":2026},[600,2624,2625],{"encoding":602},"3{,}5\\,\\%",[577,2627,2629],{"className":2628,"ariaHidden":607},[606],[577,2630,2632,2636,2640,2646,2649,2652],{"className":2631},[611],[577,2633],{"className":2634,"style":2635},[615],"height:0.9444em;vertical-align:-0.1944em;",[577,2637,2639],{"className":2638},[620],"3",[577,2641,2643],{"className":2642},[620],[577,2644,2238],{"className":2645},[2237],[577,2647,2021],{"className":2648},[620],[577,2650],{"className":2651,"style":2002},[1120],[577,2653,2027],{"className":2654},[620]," und ",[577,2657,2659,2673],{"className":2658},[580],[577,2660,2662],{"className":2661},[584],[586,2663,2664],{"xmlns":588},[590,2665,2666,2671],{},[593,2667,2668],{},[697,2669,2670],{},"25",[600,2672,2670],{"encoding":602},[577,2674,2676],{"className":2675,"ariaHidden":607},[606],[577,2677,2679,2682],{"className":2678},[611],[577,2680],{"className":2681,"style":1995},[615],[577,2683,2670],{"className":2684},[620]," Jahren Laufzeit:",[577,2687,2689],{"className":2688},[1348],[577,2690,2692,2758],{"className":2691},[580],[577,2693,2695],{"className":2694},[584],[586,2696,2697],{"xmlns":588,"display":1357},[590,2698,2699,2755],{},[593,2700,2701,2703,2705,2707,2709,2711,2713,2741,2743,2746,2748,2751,2753],{},[596,2702,598],{},[826,2704,1378],{},[697,2706,2577],{},[1977,2708,1979],{},[697,2710,1982],{},[826,2712,1058],{},[813,2714,2715,2729],{},[593,2716,2717,2724,2726],{},[818,2718,2719,2722],{},[697,2720,2721],{},"1,035",[697,2723,2670],{},[826,2725,1058],{},[697,2727,2728],{},"0,035",[593,2730,2731,2737,2739],{},[818,2732,2733,2735],{},[697,2734,2721],{},[697,2736,2670],{},[826,2738,834],{},[697,2740,837],{},[826,2742,2137],{},[697,2744,2745],{},"12",[1977,2747,1979],{},[697,2749,2750],{},"134,81",[1977,2752,1979],{},[1977,2754,2145],{},[600,2756,2757],{"encoding":602},"A = 200\\,000 \\cdot \\frac{1{,}035^{25} \\cdot 0{,}035}{1{,}035^{25} - 1} \\approx 12\\,134{,}81\\,\\text{Euro}",[577,2759,2761,2779,2803,2997],{"className":2760,"ariaHidden":607},[606],[577,2762,2764,2767,2770,2773,2776],{"className":2763},[611],[577,2765],{"className":2766,"style":616},[615],[577,2768,598],{"className":2769},[620,621],[577,2771],{"className":2772,"style":1559},[1120],[577,2774,1378],{"className":2775},[1563],[577,2777],{"className":2778,"style":1559},[1120],[577,2780,2782,2785,2788,2791,2794,2797,2800],{"className":2781},[611],[577,2783],{"className":2784,"style":1995},[615],[577,2786,2577],{"className":2787},[620],[577,2789],{"className":2790,"style":2002},[1120],[577,2792,1982],{"className":2793},[620],[577,2795],{"className":2796,"style":1121},[1120],[577,2798,1058],{"className":2799},[938],[577,2801],{"className":2802,"style":1121},[1120],[577,2804,2806,2809,2988,2991,2994],{"className":2805},[611],[577,2807],{"className":2808,"style":2200},[615],[577,2810,2812,2815,2985],{"className":2811},[620],[577,2813],{"className":2814},[872,873],[577,2816,2818],{"className":2817},[813],[577,2819,2821,2977],{"className":2820},[727,728],[577,2822,2824,2974],{"className":2823},[732],[577,2825,2827,2892,2900],{"className":2826,"style":2219},[736],[577,2828,2829,2832],{"style":1613},[577,2830],{"className":2831,"style":893},[744],[577,2833,2835,2838,2844,2848,2880,2883,2886,2889],{"className":2834},[620],[577,2836,837],{"className":2837},[620],[577,2839,2841],{"className":2840},[620],[577,2842,2238],{"className":2843},[2237],[577,2845,2847],{"className":2846},[620],"03",[577,2849,2851,2854],{"className":2850},[620],[577,2852,2021],{"className":2853},[620],[577,2855,2857],{"className":2856},[723],[577,2858,2860],{"className":2859},[727],[577,2861,2863],{"className":2862},[732],[577,2864,2866],{"className":2865,"style":2260},[736],[577,2867,2868,2871],{"style":1852},[577,2869],{"className":2870,"style":745},[744],[577,2872,2874],{"className":2873},[749,750,751,752],[577,2875,2877],{"className":2876},[620,752],[577,2878,2670],{"className":2879},[620,752],[577,2881],{"className":2882,"style":1121},[1120],[577,2884,834],{"className":2885},[938],[577,2887],{"className":2888,"style":1121},[1120],[577,2890,837],{"className":2891},[620],[577,2893,2894,2897],{"style":944},[577,2895],{"className":2896,"style":893},[744],[577,2898],{"className":2899,"style":952},[951],[577,2901,2902,2905],{"style":1645},[577,2903],{"className":2904,"style":893},[744],[577,2906,2908,2911,2917,2920,2952,2955,2958,2961,2964,2970],{"className":2907},[620],[577,2909,837],{"className":2910},[620],[577,2912,2914],{"className":2913},[620],[577,2915,2238],{"className":2916},[2237],[577,2918,2847],{"className":2919},[620],[577,2921,2923,2926],{"className":2922},[620],[577,2924,2021],{"className":2925},[620],[577,2927,2929],{"className":2928},[723],[577,2930,2932],{"className":2931},[727],[577,2933,2935],{"className":2934},[732],[577,2936,2938],{"className":2937,"style":2330},[736],[577,2939,2940,2943],{"style":1156},[577,2941],{"className":2942,"style":745},[744],[577,2944,2946],{"className":2945},[749,750,751,752],[577,2947,2949],{"className":2948},[620,752],[577,2950,2670],{"className":2951},[620,752],[577,2953],{"className":2954,"style":1121},[1120],[577,2956,1058],{"className":2957},[938],[577,2959],{"className":2960,"style":1121},[1120],[577,2962,699],{"className":2963},[620],[577,2965,2967],{"className":2966},[620],[577,2968,2238],{"className":2969},[2237],[577,2971,2973],{"className":2972},[620],"035",[577,2975,760],{"className":2976},[759],[577,2978,2980],{"className":2979},[732],[577,2981,2983],{"className":2982,"style":1702},[736],[577,2984],{},[577,2986],{"className":2987},[1011,873],[577,2989],{"className":2990,"style":1559},[1120],[577,2992,2137],{"className":2993},[1563],[577,2995],{"className":2996,"style":1559},[1120],[577,2998,3000,3003,3006,3009,3013,3019,3023,3026],{"className":2999},[611],[577,3001],{"className":3002,"style":2393},[615],[577,3004,2745],{"className":3005},[620],[577,3007],{"className":3008,"style":2002},[1120],[577,3010,3012],{"className":3011},[620],"134",[577,3014,3016],{"className":3015},[620],[577,3017,2238],{"className":3018},[2237],[577,3020,3022],{"className":3021},[620],"81",[577,3024],{"className":3025,"style":2002},[1120],[577,3027,3029],{"className":3028},[620,2414],[577,3030,2145],{"className":3031},[620],[565,3033,3034,3035,3076,3077,3105],{},"Das sind etwa ",[577,3036,3038,3053],{"className":3037},[580],[577,3039,3041],{"className":3040},[584],[586,3042,3043],{"xmlns":588},[590,3044,3045,3050],{},[593,3046,3047],{},[697,3048,3049],{},"1011,23",[600,3051,3052],{"encoding":602},"1011{,}23",[577,3054,3056],{"className":3055,"ariaHidden":607},[606],[577,3057,3059,3062,3066,3072],{"className":3058},[611],[577,3060],{"className":3061,"style":2497},[615],[577,3063,3065],{"className":3064},[620],"1011",[577,3067,3069],{"className":3068},[620],[577,3070,2238],{"className":3071},[2237],[577,3073,3075],{"className":3074},[620],"23"," € pro Monat, wenn man die Jahresrate einfach durch ",[577,3078,3080,3093],{"className":3079},[580],[577,3081,3083],{"className":3082},[584],[586,3084,3085],{"xmlns":588},[590,3086,3087,3091],{},[593,3088,3089],{},[697,3090,2745],{},[600,3092,2745],{"encoding":602},[577,3094,3096],{"className":3095,"ariaHidden":607},[606],[577,3097,3099,3102],{"className":3098},[611],[577,3100],{"className":3101,"style":1995},[615],[577,3103,2745],{"className":3104},[620]," teilt. Banken rechnen bei Monatsraten genauer mit monatlicher Verzinsung, das Ergebnis weicht dann leicht ab.",[560,3107,3109],{"id":3108},"typische-fehler","Typische Fehler",[624,3111,3112,3380,3512],{},[627,3113,3114,3115,3261,3262,3340,3341,3379],{},"Nur die Zinsen des ersten Jahres und die Tilgung ",[577,3116,3118,3140],{"className":3117},[580],[577,3119,3121],{"className":3120},[584],[586,3122,3123],{"xmlns":588},[590,3124,3125,3137],{},[593,3126,3127],{},[813,3128,3129,3135],{},[691,3130,3131,3133],{},[596,3132,695],{},[697,3134,699],{},[596,3136,661],{},[600,3138,3139],{"encoding":602},"\\frac{K_0}{n}",[577,3141,3143],{"className":3142,"ariaHidden":607},[606],[577,3144,3146,3150],{"className":3145},[611],[577,3147],{"className":3148,"style":3149},[615],"height:1.2334em;vertical-align:-0.345em;",[577,3151,3153,3156,3258],{"className":3152},[620],[577,3154],{"className":3155},[872,873],[577,3157,3159],{"className":3158},[813],[577,3160,3162,3249],{"className":3161},[727,728],[577,3163,3165,3246],{"className":3164},[732],[577,3166,3169,3183,3191],{"className":3167,"style":3168},[736],"height:0.8884em;",[577,3170,3171,3174],{"style":889},[577,3172],{"className":3173,"style":893},[744],[577,3175,3177],{"className":3176},[749,750,751,752],[577,3178,3180],{"className":3179},[620,752],[577,3181,661],{"className":3182},[620,621,752],[577,3184,3185,3188],{"style":944},[577,3186],{"className":3187,"style":893},[744],[577,3189],{"className":3190,"style":952},[951],[577,3192,3194,3197],{"style":3193},"top:-3.4101em;",[577,3195],{"className":3196,"style":893},[744],[577,3198,3200],{"className":3199},[749,750,751,752],[577,3201,3203],{"className":3202},[620,752],[577,3204,3206,3209],{"className":3205},[620,752],[577,3207,695],{"className":3208,"style":719},[620,621,752],[577,3210,3212],{"className":3211},[723],[577,3213,3215,3237],{"className":3214},[727,728],[577,3216,3218,3234],{"className":3217},[732],[577,3219,3222],{"className":3220,"style":3221},[736],"height:0.3173em;",[577,3223,3225,3228],{"style":3224},"top:-2.357em;margin-left:-0.0715em;margin-right:0.0714em;",[577,3226],{"className":3227,"style":926},[744],[577,3229,3231],{"className":3230},[749,930,931,752],[577,3232,699],{"className":3233},[620,752],[577,3235,760],{"className":3236},[759],[577,3238,3240],{"className":3239},[732],[577,3241,3244],{"className":3242,"style":3243},[736],"height:0.143em;",[577,3245],{},[577,3247,760],{"className":3248},[759],[577,3250,3252],{"className":3251},[732],[577,3253,3256],{"className":3254,"style":3255},[736],"height:0.345em;",[577,3257],{},[577,3259],{"className":3260},[1011,873]," addieren. Das ergibt ",[577,3263,3265,3291],{"className":3264},[580],[577,3266,3268],{"className":3267},[584],[586,3269,3270],{"xmlns":588},[590,3271,3272,3288],{},[593,3273,3274,3277,3280,3283,3285],{},[697,3275,3276],{},"500",[826,3278,3279],{},"+",[697,3281,3282],{},"2000",[826,3284,1378],{},[697,3286,3287],{},"2500",[600,3289,3290],{"encoding":602},"500 + 2000 = 2500",[577,3292,3294,3313,3331],{"className":3293,"ariaHidden":607},[606],[577,3295,3297,3301,3304,3307,3310],{"className":3296},[611],[577,3298],{"className":3299,"style":3300},[615],"height:0.7278em;vertical-align:-0.0833em;",[577,3302,3276],{"className":3303},[620],[577,3305],{"className":3306,"style":1121},[1120],[577,3308,3279],{"className":3309},[938],[577,3311],{"className":3312,"style":1121},[1120],[577,3314,3316,3319,3322,3325,3328],{"className":3315},[611],[577,3317],{"className":3318,"style":1995},[615],[577,3320,3282],{"className":3321},[620],[577,3323],{"className":3324,"style":1559},[1120],[577,3326,1378],{"className":3327},[1563],[577,3329],{"className":3330,"style":1559},[1120],[577,3332,3334,3337],{"className":3333},[611],[577,3335],{"className":3336,"style":1995},[615],[577,3338,3287],{"className":3339},[620]," € statt ",[577,3342,3344,3358],{"className":3343},[580],[577,3345,3347],{"className":3346},[584],[586,3348,3349],{"xmlns":588},[590,3350,3351,3355],{},[593,3352,3353],{},[697,3354,2140],{},[600,3356,3357],{"encoding":602},"2309{,}75",[577,3359,3361],{"className":3360,"ariaHidden":607},[606],[577,3362,3364,3367,3370,3376],{"className":3363},[611],[577,3365],{"className":3366,"style":2497},[615],[577,3368,2397],{"className":3369},[620],[577,3371,3373],{"className":3372},[620],[577,3374,2238],{"className":3375},[2237],[577,3377,2407],{"className":3378},[620]," €, denn die Zinsen sinken mit der Restschuld.",[627,3381,3382,3441,3442,3511],{},[577,3383,3385,3403],{"className":3384},[580],[577,3386,3388],{"className":3387},[584],[586,3389,3390],{"xmlns":588},[590,3391,3392,3400],{},[593,3393,3394],{},[818,3395,3396,3398],{},[596,3397,822],{},[596,3399,661],{},[600,3401,3402],{"encoding":602},"q^n",[577,3404,3406],{"className":3405,"ariaHidden":607},[606],[577,3407,3409,3412],{"className":3408},[611],[577,3410],{"className":3411,"style":1134},[615],[577,3413,3415,3418],{"className":3414},[620],[577,3416,822],{"className":3417,"style":906},[620,621],[577,3419,3421],{"className":3420},[723],[577,3422,3424],{"className":3423},[727],[577,3425,3427],{"className":3426},[732],[577,3428,3430],{"className":3429,"style":1153},[736],[577,3431,3432,3435],{"style":1156},[577,3433],{"className":3434,"style":745},[744],[577,3436,3438],{"className":3437},[749,750,751,752],[577,3439,661],{"className":3440},[620,621,752]," im Zähler vergessen. Dann erhält man die Rate eines Sparplans mit Endwert ",[577,3443,3445,3462],{"className":3444},[580],[577,3446,3448],{"className":3447},[584],[586,3449,3450],{"xmlns":588},[590,3451,3452,3460],{},[593,3453,3454],{},[691,3455,3456,3458],{},[596,3457,695],{},[697,3459,699],{},[600,3461,702],{"encoding":602},[577,3463,3465],{"className":3464,"ariaHidden":607},[606],[577,3466,3468,3471],{"className":3467},[611],[577,3469],{"className":3470,"style":712},[615],[577,3472,3474,3477],{"className":3473},[620],[577,3475,695],{"className":3476,"style":719},[620,621],[577,3478,3480],{"className":3479},[723],[577,3481,3483,3503],{"className":3482},[727,728],[577,3484,3486,3500],{"className":3485},[732],[577,3487,3489],{"className":3488,"style":737},[736],[577,3490,3491,3494],{"style":740},[577,3492],{"className":3493,"style":745},[744],[577,3495,3497],{"className":3496},[749,750,751,752],[577,3498,699],{"className":3499},[620,752],[577,3501,760],{"className":3502},[759],[577,3504,3506],{"className":3505},[732],[577,3507,3509],{"className":3508,"style":767},[736],[577,3510],{},".",[627,3513,3514,3515,3544,3545,3646,3647,3685,3686,3511],{},"Mit ",[577,3516,3518,3531],{"className":3517},[580],[577,3519,3521],{"className":3520},[584],[586,3522,3523],{"xmlns":588},[590,3524,3525,3529],{},[593,3526,3527],{},[596,3528,565],{},[600,3530,565],{"encoding":602},[577,3532,3534],{"className":3533,"ariaHidden":607},[606],[577,3535,3537,3541],{"className":3536},[611],[577,3538],{"className":3539,"style":3540},[615],"height:0.625em;vertical-align:-0.1944em;",[577,3542,565],{"className":3543},[620,621]," statt mit ",[577,3546,3548,3567],{"className":3547},[580],[577,3549,3551],{"className":3550},[584],[586,3552,3553],{"xmlns":588},[590,3554,3555,3564],{},[593,3556,3557],{},[813,3558,3559,3561],{},[596,3560,565],{},[697,3562,3563],{},"100",[600,3565,3566],{"encoding":602},"\\frac{p}{100}",[577,3568,3570],{"className":3569,"ariaHidden":607},[606],[577,3571,3573,3577],{"className":3572},[611],[577,3574],{"className":3575,"style":3576},[615],"height:1.0925em;vertical-align:-0.345em;",[577,3578,3580,3583,3643],{"className":3579},[620],[577,3581],{"className":3582},[872,873],[577,3584,3586],{"className":3585},[813],[577,3587,3589,3635],{"className":3588},[727,728],[577,3590,3592,3632],{"className":3591},[732],[577,3593,3596,3610,3618],{"className":3594,"style":3595},[736],"height:0.7475em;",[577,3597,3598,3601],{"style":889},[577,3599],{"className":3600,"style":893},[744],[577,3602,3604],{"className":3603},[749,750,751,752],[577,3605,3607],{"className":3606},[620,752],[577,3608,3563],{"className":3609},[620,752],[577,3611,3612,3615],{"style":944},[577,3613],{"className":3614,"style":893},[744],[577,3616],{"className":3617,"style":952},[951],[577,3619,3620,3623],{"style":1285},[577,3621],{"className":3622,"style":893},[744],[577,3624,3626],{"className":3625},[749,750,751,752],[577,3627,3629],{"className":3628},[620,752],[577,3630,565],{"className":3631},[620,621,752],[577,3633,760],{"className":3634},[759],[577,3636,3638],{"className":3637},[732],[577,3639,3641],{"className":3640,"style":3255},[736],[577,3642],{},[577,3644],{"className":3645},[1011,873]," rechnen: Bei ",[577,3648,3650,3667],{"className":3649},[580],[577,3651,3653],{"className":3652},[584],[586,3654,3655],{"xmlns":588},[590,3656,3657,3665],{},[593,3658,3659,3661,3663],{},[697,3660,2021],{},[1977,3662,1979],{},[596,3664,2027],{"mathvariant":2026},[600,3666,2030],{"encoding":602},[577,3668,3670],{"className":3669,"ariaHidden":607},[606],[577,3671,3673,3676,3679,3682],{"className":3672},[611],[577,3674],{"className":3675,"style":2040},[615],[577,3677,2021],{"className":3678},[620],[577,3680],{"className":3681,"style":2002},[1120],[577,3683,2027],{"className":3684},[620]," ist ",[577,3687,3689,3711],{"className":3688},[580],[577,3690,3692],{"className":3691},[584],[586,3693,3694],{"xmlns":588},[590,3695,3696,3708],{},[593,3697,3698,3700,3702,3704,3706],{},[596,3699,822],{},[826,3701,834],{},[697,3703,837],{},[826,3705,1378],{},[697,3707,2122],{},[600,3709,3710],{"encoding":602},"q - 1 = 0{,}05",[577,3712,3714,3733,3751],{"className":3713,"ariaHidden":607},[606],[577,3715,3717,3721,3724,3727,3730],{"className":3716},[611],[577,3718],{"className":3719,"style":3720},[615],"height:0.7778em;vertical-align:-0.1944em;",[577,3722,822],{"className":3723,"style":906},[620,621],[577,3725],{"className":3726,"style":1121},[1120],[577,3728,834],{"className":3729},[938],[577,3731],{"className":3732,"style":1121},[1120],[577,3734,3736,3739,3742,3745,3748],{"className":3735},[611],[577,3737],{"className":3738,"style":1995},[615],[577,3740,837],{"className":3741},[620],[577,3743],{"className":3744,"style":1559},[1120],[577,3746,1378],{"className":3747},[1563],[577,3749],{"className":3750,"style":1559},[1120],[577,3752,3754,3757,3760,3766],{"className":3753},[611],[577,3755],{"className":3756,"style":2497},[615],[577,3758,699],{"className":3759},[620],[577,3761,3763],{"className":3762},[620],[577,3764,2238],{"className":3765},[2237],[577,3767,2363],{"className":3768},[620],{"title":3770,"searchDepth":3771,"depth":3771,"links":3772},"",2,[3773,3774,3775,3776],{"id":562,"depth":3771,"text":563},{"id":1033,"depth":3771,"text":1034},{"id":1956,"depth":3771,"text":1957},{"id":3108,"depth":3771,"text":3109},[3778,3780,3782,3785,3788,3791,3794,3797],{"lhs":3779,"rhs":695},"(K*q^n*(q - 1)\u002F(q^n - 1)) * (q^n - 1)\u002F(q^n*(q - 1))",{"lhs":3781,"rhs":699},"K*q^3 - (K*q^3*(q - 1)\u002F(q^3 - 1)) * (q^3 - 1)\u002F(q - 1)",{"lhs":3783,"rhs":3784},"round(10000 * 1.05^5 * 0.05 \u002F (1.05^5 - 1), 2)","2309.75",{"lhs":3786,"rhs":3787},"round(5 * 10000 * 1.05^5 * 0.05 \u002F (1.05^5 - 1), 2)","11548.74",{"lhs":3789,"rhs":3790},"round(5 * 10000 * 1.05^5 * 0.05 \u002F (1.05^5 - 1) - 10000, 2)","1548.74",{"lhs":3792,"rhs":3793},"round(200000 * 1.035^25 * 0.035 \u002F (1.035^25 - 1), 2)","12134.81",{"lhs":3795,"rhs":3796},"round(200000 * 1.035^25 * 0.035 \u002F (1.035^25 - 1) \u002F 12, 2)","1011.23",{"lhs":3798,"rhs":3287},"10000*0.05 + 10000\u002F5","p > 0,\\ n \\geq 1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p > 0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7335em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\geq 1\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","annuity-payment","A = K_0 \\cdot \\frac{q^n \\cdot (q - 1)}{q^n - 1}, \\qquad q = 1 + \\frac{p}{100}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>K\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmsup>\u003Cmi>q\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>q\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmsup>\u003Cmi>q\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmi>q\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>+\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>100\u003C\u002Fmn>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = K_0 \\cdot \\frac{q^n \\cdot (q - 1)}{q^n - 1}, \\qquad q = 1 + \\frac{p}{100}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\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:2.3074em;vertical-align:-0.8804em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.427em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.5904em;\">\u003Cspan style=\"top:-2.989em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6644em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8804em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:2em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7278em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.7936em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1076em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">100\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Farithmetic\u002Fannuitaet",[],[3812,3813,3814],"loan-amortization","annuity-present-value","compound-interest",{"title":548,"description":3770},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fannuitaet","Die Annuität ist die feste Jahresrate, mit der ein Kredit K₀ samt Zinsen in n Jahren genau zurückgezahlt wird.",[3819,3820,3821,3822,3823],"kredit","darlehen","rate","tilgung","finanzmathematik",[3825,3828,3831,3834,3837],{"symbol":598,"meaning":3826,"symbolHtml":3827},"Annuität, die gleichbleibende jährliche Rate aus Zinsen und Tilgung","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":702,"meaning":3829,"symbolHtml":3830},"Kreditbetrag (Darlehenssumme) zu Beginn","\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\" 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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":661,"meaning":3838,"symbolHtml":3839},"Laufzeit in Jahren, nach der der Kredit vollständig getilgt ist","\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 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