Question

You have an initial amortizing loan (similar to a mortgage) of $25,000 to be repaid in equal 30 payments, over 30years. The annual interest rate is 8%. What is the amount of interest you will pay at the end of year 16?

1. 15,206

2. 14,041

3. 15,724

4. 14646

Answer 1

We can use following Present Value of an Annuity formula to calculate the annual loan payment with 8% interest rate on the loan

PV of loan = PMT * [1-(1+i) ^-n)]/i

Where

Present value of loan (PV) = $25,000

Monthly loan payment PMT =?

Number of payments n = 30 (years)

Annual interest rate I =8%

Therefore

$25,000 = PMT * [1- (1+8%) ^-30]/8%

Or PMT = $2,220.69

Now make an amortization schedule to calculate interest rate at end of each year.

Initial loan	$25,000
Annual payment =	$2,220.69
Interest rate =	8%
Time period	30 years
Amortization Chart
Year	Interest @ 8% of new balance of previous period	Payment (PMT on Loan)	New Balance (Previous balance+ Interest - Payment)
0	$0.00	$0.00	$25,000.00
1	$2,000.00	$2,220.69	$24,779.31
2	$1,982.35	$2,220.69	$24,540.97
3	$1,963.28	$2,220.69	$24,283.57
4	$1,942.69	$2,220.69	$24,005.56
5	$1,920.45	$2,220.69	$23,705.32
6	$1,896.43	$2,220.69	$23,381.06
7	$1,870.49	$2,220.69	$23,030.86
8	$1,842.47	$2,220.69	$22,652.65
9	$1,812.21	$2,220.69	$22,244.17
10	$1,779.53	$2,220.69	$21,803.02
11	$1,744.24	$2,220.69	$21,326.58
12	$1,706.13	$2,220.69	$20,812.02
13	$1,664.96	$2,220.69	$20,256.29
14	$1,620.50	$2,220.69	$19,656.11
15	$1,572.49	$2,220.69	$19,007.91
16	$1,520.63	$2,220.69	$18,307.86
17	$1,464.63	$2,220.69	$17,551.80
18	$1,404.14	$2,220.69	$16,735.26
19	$1,338.82	$2,220.69	$15,853.40
20	$1,268.27	$2,220.69	$14,900.98
21	$1,192.08	$2,220.69	$13,872.38
22	$1,109.79	$2,220.69	$12,761.48
23	$1,020.92	$2,220.69	$11,561.71
24	$924.94	$2,220.69	$10,265.96
25	$821.28	$2,220.69	$8,866.55
26	$709.32	$2,220.69	$7,355.19
27	$588.42	$2,220.69	$5,722.92
28	$457.83	$2,220.69	$3,960.07
29	$316.81	$2,220.69	$2,056.19
30	$164.50	$2,220.69	$0.00

The amount of interest you will pay at the end of year 16: $1,520.63 or $1,520.6