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

Finance Dec 21, 2020

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

Expert Solution

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

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