Question

Larry is repaying a loan with payments of $2,500 at the end of every two years. If the amount of interest in the fourth installment is $2,458, find the amount of principal in the seventh installment. Assume an annual effective interest rate of 13%. A) Less than $60 B) At least $60, but less than $70 C ) At leas At least $70, but less than $80 D At least $80, but less than $90 At least $90

Answer 1

Installment payment = $2,500

Interest in fourth installment = $2,458
Principal in fourth installment = $2,500 - $2,458
Principal in fourth installment = 42

Annual effective interest rate = 13%
With payments made every 2 years

Let P be the outstanding amount at after third installment is paid.
Hence the interest in the fourth installment = outstanding amount after third installment x effective annual interest rate x 2
Hence,
2,458 = P x 0.13 x 2
Hence P = 9,453.87

From this, we build a loan amortization schedule as follows

Interest rate	13%
	Payment	Interest	Principal	Outstanding
Installment 3	$        2,500			$           9,454
Installment 4	$        2,500	$    2,458	$          42	$           9,412
Installment 5	$        2,500	$    2,447	$          53	$           9,359
Installment 6	$        2,500	$    2,433	$          67	$           9,292
Installment 7	$        2,500	$    2,416	$          84	$           9,208

We see that principal repaid in the seventh installment is $84, which is more than $80 but less than $90

Hence option D is correct