Fill This Form To Receive Instant Help
Fill This Form To Receive Instant Help
Homework answers / question archive / A loan is being repaid with a first payment of 2,500 at the end of the first year and subsequent payments decreasing by 100 at the end of each year thereafter
A loan is being repaid with a first payment of 2,500 at the end of the first year and subsequent payments decreasing by 100 at the end of each year thereafter. Assuming an annual effective rate of 10%, calculate the loan amount X. Possible Answers A 11,346 B 13,615 C 15,923 D 17,396 E 18,112
The loan amount is nothing but the present value of all the loan payments discounted using the given rate of interest
We know the formula for present value future cash flow is A/(1+r)n
Where A is the future cash flow
r is the rate of interest and n is the number of periods
We can tabulate the present value of all the loan payments as below.
| Year | Cash flows | Discount Factor @ 10% | Present value |
| 1 | 2,500.00 | 0.909 | 2,272.73 |
| 2 | 2,400.00 | 0.826 | 1,983.47 |
| 3 | 2,300.00 | 0.751 | 1,728.02 |
| 4 | 2,200.00 | 0.683 | 1,502.63 |
| 5 | 2,100.00 | 0.621 | 1,303.93 |
| 6 | 2,000.00 | 0.564 | 1,128.95 |
| 7 | 1,900.00 | 0.513 | 975.00 |
| 8 | 1,800.00 | 0.467 | 839.71 |
| 9 | 1,700.00 | 0.424 | 720.97 |
| 10 | 1,600.00 | 0.386 | 616.87 |
| 11 | 1,500.00 | 0.350 | 525.74 |
| 12 | 1,400.00 | 0.319 | 446.08 |
| 13 | 1,300.00 | 0.290 | 376.56 |
| 14 | 1,200.00 | 0.263 | 316.00 |
| 15 | 1,100.00 | 0.239 | 263.33 |
| 16 | 1,000.00 | 0.218 | 217.63 |
| 17 | 900.00 | 0.198 | 178.06 |
| 18 | 800.00 | 0.180 | 143.89 |
| 19 | 700.00 | 0.164 | 114.46 |
| 20 | 600.00 | 0.149 | 89.19 |
| 21 | 500.00 | 0.135 | 67.57 |
| 22 | 400.00 | 0.123 | 49.14 |
| 23 | 300.00 | 0.112 | 33.50 |
| 24 | 200.00 | 0.102 | 20.31 |
| 25 | 100.00 | 0.092 | 9.23 |
| Value of laon | 15,922.96 |
Hence the amount of loan is 15.923
