In[]:=
interest=1+3/100/12//N
Out[]=
1.0025
In[]:=
balance[period_]:=​​interest*balance[period-1]-payment;​​balance[0]=430000;​​Expand[balance[20*12]]
Out[]=
782925.-328.302payment
In[]:=
equation=(balance[20*12]//Expand)==0
Out[]=
782925.-328.302payment0
In[]:=
Solve[equation,payment]//Flatten
Out[]=
{payment2384.77}
In[]:=
payment=payment/.%
Out[]=
2384.77
In[]:=
payment
Out[]=
2384.77
In[]:=
​​unpaidBalance=Table[balance[k],{k,1,240}]
Out[]=
{428690.,427377.,426061.,424741.,423418.,422092.,420763.,419430.,418094.,416754.,415411.,414065.,412715.,411362.,410006.,408646.,407283.,405916.,404546.,403173.,401796.,400416.,399032.,397645.,396254.,394860.,393463.,392061.,390657.,389249.,387837.,386422.,385003.,383581.,382155.,380726.,379293.,377856.,376416.,374972.,373525.,372074.,370619.,369161.,367699.,366234.,364765.,363292.,361815.,360335.,358851.,357364.,355872.,354377.,352878.,351376.,349869.,348359.,346845.,345328.,343806.,342281.,340752.,339219.,337682.,336142.,334597.,333049.,331497.,329941.,328381.,326817.,325249.,323678.,322102.,320523.,318939.,317352.,315760.,314165.,312566.,310962.,309355.,307744.,306128.,304509.,302885.,301258.,299626.,297990.,296351.,294707.,293059.,291407.,289750.,288090.,286425.,284757.,283084.,281407.,279725.,278040.,276350.,274656.,272958.,271256.,269549.,267838.,266123.,264404.,262680.,260952.,259220.,257483.,255742.,253996.,252247.,250492.,248734.,246971.,245204.,243432.,241656.,239875.,238090.,236300.,234506.,232708.,230905.,229097.,227285.,225469.,223648.,221822.,219992.,218157.,216318.,214474.,212625.,210772.,208914.,207052.,205184.,203313.,201436.,199555.,197669.,195778.,193883.,191983.,190078.,188169.,186254.,184335.,182411.,180483.,178549.,176611.,174667.,172719.,170766.,168808.,166846.,164878.,162905.,160928.,158945.,156958.,154966.,152968.,150966.,148959.,146946.,144929.,142906.,140879.,138846.,136809.,134766.,132718.,130665.,128607.,126544.,124475.,122402.,120323.,118239.,116150.,114055.,111956.,109851.,107741.,105625.,103505.,101379.,99247.3,97110.7,94968.7,92821.3,90668.6,88510.5,86347.,84178.1,82003.8,79824.,77638.8,75448.2,73252.,71050.4,68843.2,66630.6,64412.4,62188.6,59959.3,57724.5,55484.,53237.9,50986.3,48729.,46466.,44197.4,41923.1,39643.2,37357.5,35066.1,32769.,30466.2,28157.6,25843.2,23523.,21197.1,18865.3,16527.7,14184.2,11834.9,9479.76,7118.69,4751.71,2378.82,3.67072×
-9
10
}
In[]:=
unpaidBalanceReduction=​​Table[balance[k]-balance[k+1],{k,0,239}]
Out[]=
{1309.77,1313.04,1316.33,1319.62,1322.92,1326.22,1329.54,1332.86,1336.2,1339.54,1342.88,1346.24,1349.61,1352.98,1356.36,1359.75,1363.15,1366.56,1369.98,1373.4,1376.84,1380.28,1383.73,1387.19,1390.66,1394.13,1397.62,1401.11,1404.62,1408.13,1411.65,1415.18,1418.71,1422.26,1425.82,1429.38,1432.96,1436.54,1440.13,1443.73,1447.34,1450.96,1454.58,1458.22,1461.87,1465.52,1469.18,1472.86,1476.54,1480.23,1483.93,1487.64,1491.36,1495.09,1498.83,1502.57,1506.33,1510.1,1513.87,1517.66,1521.45,1525.25,1529.07,1532.89,1536.72,1540.56,1544.42,1548.28,1552.15,1556.03,1559.92,1563.82,1567.73,1571.65,1575.58,1579.51,1583.46,1587.42,1591.39,1595.37,1599.36,1603.36,1607.36,1611.38,1615.41,1619.45,1623.5,1627.56,1631.63,1635.7,1639.79,1643.89,1648.,1652.12,1656.25,1660.39,1664.54,1668.71,1672.88,1677.06,1681.25,1685.46,1689.67,1693.89,1698.13,1702.37,1706.63,1710.9,1715.17,1719.46,1723.76,1728.07,1732.39,1736.72,1741.06,1745.42,1749.78,1754.15,1758.54,1762.94,1767.34,1771.76,1776.19,1780.63,1785.08,1789.54,1794.02,1798.5,1803.,1807.51,1812.03,1816.56,1821.1,1825.65,1830.21,1834.79,1839.38,1843.98,1848.59,1853.21,1857.84,1862.48,1867.14,1871.81,1876.49,1881.18,1885.88,1890.6,1895.32,1900.06,1904.81,1909.57,1914.35,1919.13,1923.93,1928.74,1933.56,1938.4,1943.24,1948.1,1952.97,1957.85,1962.75,1967.66,1972.57,1977.51,1982.45,1987.41,1992.37,1997.36,2002.35,2007.35,2012.37,2017.4,2022.45,2027.5,2032.57,2037.65,2042.75,2047.85,2052.97,2058.11,2063.25,2068.41,2073.58,2078.77,2083.96,2089.17,2094.4,2099.63,2104.88,2110.14,2115.42,2120.71,2126.01,2131.32,2136.65,2141.99,2147.35,2152.72,2158.1,2163.49,2168.9,2174.32,2179.76,2185.21,2190.67,2196.15,2201.64,2207.14,2212.66,2218.19,2223.74,2229.3,2234.87,2240.46,2246.06,2251.67,2257.3,2262.95,2268.6,2274.28,2279.96,2285.66,2291.38,2297.1,2302.85,2308.6,2314.38,2320.16,2325.96,2331.78,2337.61,2343.45,2349.31,2355.18,2361.07,2366.97,2372.89,2378.82}
portionToInterest=​​payment-unpaidBalanceReduction(*portiontoprincipal*)
Out[]=
{1075.,1071.73,1068.44,1065.15,1061.85,1058.55,1055.23,1051.91,1048.57,1045.23,1041.88,1038.53,1035.16,1031.79,1028.41,1025.01,1021.62,1018.21,1014.79,1011.37,1007.93,1004.49,1001.04,997.58,994.112,990.636,987.151,983.656,980.154,976.642,973.122,969.593,966.055,962.508,958.952,955.388,951.814,948.232,944.641,941.04,937.431,933.813,930.185,926.549,922.903,919.249,915.585,911.912,908.23,904.538,900.838,897.128,893.409,889.68,885.943,882.196,878.439,874.673,870.898,867.113,863.319,859.516,855.702,851.88,848.048,844.206,840.354,836.493,832.623,828.742,824.852,820.952,817.043,813.124,809.194,805.256,801.307,797.348,793.38,789.401,785.413,781.414,777.406,773.387,769.359,765.32,761.272,757.213,753.144,749.065,744.976,740.876,736.767,732.647,728.516,724.376,720.225,716.063,711.892,707.709,703.517,699.314,695.1,690.876,686.641,682.396,678.14,673.873,669.596,665.308,661.009,656.7,652.38,648.049,643.707,639.354,634.991,630.616,626.231,621.835,617.427,613.009,608.58,604.139,599.688,595.225,590.751,586.266,581.77,577.262,572.743,568.213,563.672,559.119,554.555,549.98,545.393,540.794,536.184,531.563,526.93,522.285,517.629,512.961,508.281,503.59,498.887,494.173,489.446,484.708,479.958,475.196,470.422,465.636,460.838,456.028,451.206,446.372,441.526,436.668,431.798,426.916,422.021,417.114,412.195,407.264,402.32,397.364,392.395,387.414,382.421,377.415,372.397,367.366,362.322,357.266,352.197,347.116,342.022,336.915,331.795,326.663,321.517,316.359,311.188,306.004,300.807,295.598,290.375,285.139,279.89,274.627,269.352,264.063,258.762,253.447,248.118,242.777,237.422,232.053,226.672,221.276,215.868,210.445,205.009,199.56,194.097,188.62,183.13,177.626,172.108,166.576,161.031,155.472,149.898,144.311,138.71,133.095,127.466,121.822,116.165,110.494,104.808,99.1079,93.3938,87.6653,81.9226,76.1655,70.394,64.608,58.8076,52.9927,47.1633,41.3192,35.4606,29.5873,23.6994,17.7967,11.8793,5.94706}
In[]:=
Length[portionToInterest]
Out[]=
240
In[]:=
Length[unpaidBalance]
Out[]=
240
In[]:=
Length[unpaidBalanceReduction]
Out[]=
240
In[]:=
AmortizationTable=​​Table[{n,NumberForm[payment,{Infinity,2}],​​NumberForm[portionToInterest[[n]],​​{Infinity,2}],​​NumberForm[unpaidBalanceReduction[[n]],​​{Infinity,2}],​​NumberForm[unpaidBalance[[n]],​​{Infinity,2}]},{n,1,240}]
Out[]=
In[]:=
AmortizationTable[[-1]][[-1]]="0.00"
Out[]=
0.00
In[]:=
AmortizationTable
In[]:=
AmortizationTable=​​Prepend[AmortizationTable,{"Payment\nNumber\n","Payment\n","Interest\n","Unpaid\nBalance\nReduction\n","Unpaid Balance\n"}]
$RecursionLimit
:Recursion depth of 1024 exceeded during evaluation of Prepend[AmortizationTable,{PaymentNumber,Payment,Interest,UnpaidBalanceReduction,Unpaid Balance}].
Out[]=
Hold[AmortizationTable=Prepend[AmortizationTable,{PaymentNumber,Payment,Interest,UnpaidBalanceReduction,Unpaid Balance}]]