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Homework answers / question archive / A car loan of $20,000 at a nominal rate r=9% compounded monthly for 48 months requires equal payments at the end each month

A car loan of $20,000 at a nominal rate r=9% compounded monthly for 48 months requires equal payments at the end each month

Economics

A car loan of $20,000 at a nominal rate r=9% compounded monthly for 48 months requires equal payments at the end each month. What will be the monthly payment A=_ ? What will be the interest payment (In), principal payment (Pn) and remaining balance (Bn) for the first payment (month 1) and the second payment (month 2) respectively? End of Month Interest Payment Repayment of Principal In Pn n Remaining Loan Balance B. $20,000 Bi=? B2=? 0 1,=? 1 2 P1=? P2=? 12=?

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Loan amount (P) = 20,000

Interest rate (r) = 9% compounded monthly which means monthly interest rate is 9% / 12 = 0.0075

Duration of loan (n) = 48 months

EMI = [P * r * (1 + r)^n] / [(1 + r)^n - 1]

EMI = [20,000 * 0.0075 * (1 + 0.0075)^48] / [(1 + 0.0075)^48 - 1] = 497.70

Here is the complete loan sheet:

End of month Payment made Interest payment Repayment of principle Remaininig loan balance
0                                 20,000.00
1               497.70                   150.00                               347.70                           19,652.30
2               497.70                   147.39                               350.31                           19,301.99
3               497.70                   144.76                               352.94                           18,949.06
4               497.70                   142.12                               355.58                           18,593.47
5               497.70                   139.45                               358.25                           18,235.22
6               497.70                   136.76                               360.94                           17,874.29
7               497.70                   134.06                               363.64                           17,510.65
8               497.70                   131.33                               366.37                           17,144.28
9               497.70                   128.58                               369.12                           16,775.16
10               497.70                   125.81                               371.89                           16,403.27
11               497.70                   123.02                               374.68                           16,028.59
12               497.70                   120.21                               377.49                           15,651.11
13               497.70                   117.38                               380.32                           15,270.79
14               497.70                   114.53                               383.17                           14,887.62
15               497.70                   111.66                               386.04                           14,501.58
16               497.70                   108.76                               388.94                           14,112.64
17               497.70                   105.84                               391.86                           13,720.79
18               497.70                   102.91                               394.79                           13,325.99
19               497.70                      99.94                               397.76                           12,928.24
20               497.70                      96.96                               400.74                           12,527.50
21               497.70                      93.96                               403.74                           12,123.75
22               497.70                      90.93                               406.77                           11,716.98
23               497.70                      87.88                               409.82                           11,307.16
24               497.70                      84.80                               412.90                           10,894.26
25               497.70                      81.71                               415.99                           10,478.27
26               497.70                      78.59                               419.11                           10,059.16
27               497.70                      75.44                               422.26                              9,636.90
28               497.70                      72.28                               425.42                              9,211.48
29               497.70                      69.09                               428.61                              8,782.86
30               497.70                      65.87                               431.83                              8,351.03
31               497.70                      62.63                               435.07                              7,915.96
32               497.70                      59.37                               438.33                              7,477.63
33               497.70                      56.08                               441.62                              7,036.02
34               497.70                      52.77                               444.93                              6,591.09
35               497.70                      49.43                               448.27                              6,142.82
36               497.70                      46.07                               451.63                              5,691.19
37               497.70                      42.68                               455.02                              5,236.17
38               497.70                      39.27                               458.43                              4,777.74
39               497.70                      35.83                               461.87                              4,315.88
40               497.70                      32.37                               465.33                              3,850.55
41               497.70                      28.88                               468.82                              3,381.73
42               497.70                      25.36                               472.34                              2,909.39
43               497.70                      21.82                               475.88                              2,433.51
44               497.70                      18.25                               479.45                              1,954.06
45               497.70                      14.66                               483.04                              1,471.01
46               497.70                      11.03                               486.67                                 984.35
47               497.70                        7.38                               490.32                                 494.03
48               497.70                        3.70                               494.00                                     0.03

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