Homework Sourse4a You took a 5000 48month car loan with 08 nominal annual i
(4a) You took a $5,000 48-month car loan with 08% nominal annual interest rate. How much money do you still owe after the 18th payment? (Assume monthly compounding on your interest rate and equal monthly payment).
Solution
Monthly (nominal) interest rate = 8%/12 = 0.67%
Monthly payment ($) = Loan amount / P/A(r%, N) = 5,000 / P/A(0.67%, 48) = 5,000 / 40.9304** = 122.16
Interest payment in month N = Beginning balance in month N x 0.0067
Principal payment in month N = $122.16 - Interest payment in month N
Loan repayment schedule for first 18 months is as follows.
Money owed after 18th payment = $2,801.12
**P/A(r*%, N) = [1 - (1 + r)-N] / r
P/A(0.67%, 48) = [1 - (1.0067)-48] / 0.0067 = (1 - 0.7258) / 0.0067 = 0.2742 / 0.0067 = 40.9304
| Month | Beginning balance ($) | Monthly Payment ($) | Interest Payment ($) | Principal Payment ($) | Ending Balance ($) |
| 1 | 5,000.00 | 122.16 | 33.50 | 88.66 | 4,877.84 |
| 2 | 4,877.84 | 122.16 | 32.68 | 89.48 | 4,755.68 |
| 3 | 4,755.68 | 122.16 | 31.86 | 90.30 | 4,633.52 |
| 4 | 4,633.52 | 122.16 | 31.04 | 91.12 | 4,511.36 |
| 5 | 4,511.36 | 122.16 | 30.23 | 91.93 | 4,389.20 |
| 6 | 4,389.20 | 122.16 | 29.41 | 92.75 | 4,267.04 |
| 7 | 4,267.04 | 122.16 | 28.59 | 93.57 | 4,144.88 |
| 8 | 4,144.88 | 122.16 | 27.77 | 94.39 | 4,022.72 |
| 9 | 4,022.72 | 122.16 | 26.95 | 95.21 | 3,900.56 |
| 10 | 3,900.56 | 122.16 | 26.13 | 96.03 | 3,778.40 |
| 11 | 3,778.40 | 122.16 | 25.32 | 96.84 | 3,656.24 |
| 12 | 3,656.24 | 122.16 | 24.50 | 97.66 | 3,534.08 |
| 13 | 3,534.08 | 122.16 | 23.68 | 98.48 | 3,411.92 |
| 14 | 3,411.92 | 122.16 | 22.86 | 99.30 | 3,289.76 |
| 15 | 3,289.76 | 122.16 | 22.04 | 100.12 | 3,167.60 |
| 16 | 3,167.60 | 122.16 | 21.22 | 100.94 | 3,045.44 |
| 17 | 3,045.44 | 122.16 | 20.40 | 101.76 | 2,923.28 |
| 18 | 2,923.28 | 122.16 | 19.59 | 102.57 | 2,801.12 |
