Question

A loan is repaid in nine equal annual installments. The first payment is due one year after the loan is made. The effective annual interest rate is 5%. The total amount of interest paid in the third, fourth, and fifth payments combined is $3798. What is the total amount of principal repaid in the seventh, eighth, and ninth payments combined?

Choices:

1. Less than $13,600
2. At least $13,600, but less than $13,700
3. At least $13,700, but less than $13,800
4. At least $13,800, but less than $13,900
5. $13,900 or more

Answer 1

We see that from interest paid in 3rd, 4th and 5th payment combined, the loan or principal amount is 35540.17951

Loan Amortization Schedule:

Payment	Loan beginning balance	Payment	Interest payment	Principal payment	Loan ending balance
1	35540.17951	$5,000.15	$1,777.01	$3,223.14	$32,317.04
2	$32,317.04	$5,000.15	$1,615.85	$3,384.30	$28,932.74
3	$28,932.74	$5,000.15	$1,446.64	$3,553.51	$25,379.23
4	$25,379.23	$5,000.15	$1,268.96	$3,731.19	$21,648.04
5	$21,648.04	$5,000.15	$1,082.40	$3,917.75	$17,730.29
6	$17,730.29	$5,000.15	$886.51	$4,113.64	$13,616.65
7	$13,616.65	$5,000.15	$680.83	$4,319.32	$9,297.33
8	$9,297.33	$5,000.15	$464.87	$4,535.28	$4,762.05
9	$4,762.05	$5,000.15	$238.10	$4,762.05	$0.00

Total principal paid in 7th, 8th and 9th payment combined= 13616.65

Hence, At least $13,600, but less than $13,700