Question

Two loans, both of an amount of 720,000 are repaid at a nominal interest
rate of 19.2% convertible monthly. Loan 1 is to be repaid with 360 level monthly
payments. Loan 2 is to be repaid by 360 monthly payments, each containing
equal principal amounts and an interest amount based on the unpaid balance.
Payments are made at the end of each month for both loans. The monthly
payment for Loan 1 first exceeds the monthly payment for Loan 2 with the
kth payment. For Loan 2, what is the total interest paid in the last 360-k payments?

(a) 1,389,923
(b) 1,416, 096
(c) 1,432,035
(d) 1,581,764
(e) 1,590,370

Answer 1

1. Monthly Payment in Loan 1 = 720000 / PVAF(1.60%,360) = 720000 / 62.29 = $11558.12

2. Monthly Payment in Loan 2 = 720000/360 + Interest

the interest of month in Loan 2 where Loan 1 exceeds Loan 2

Loan 1 > Loan 2

11558.12 > (2000 + Interest)

Interest < $9558.12

Loan Balance of Loan 2 at Interest = $9558.12 / 0.016 = 597382.50

Payment made till $597382.50 = (720000 - 597382.50)/2000 = 61

Interest for 62nd payment for Loan 2 = ($720000 - 122000) * 0.192/12 = $9568

Now the interest amount will decrease with next payment by $32 (2000 * 0.192/12)

Thus Total Interest = 62nd Interest * (360 - k) - Sum of 32 ,64 .... (Arithmetic progression)

Thus Total Interest = 9568 * (360 - 61) - 1425632

Thus Total Interest = $1435200 Option C is the nearest choice

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