Question

A loan of 100,000 is being repaid by 15 equal installments made at the end of each year at 6% interest effective annually. Immediately after the eighth payment, the loan is renegotiated as follows: (i) The borrower will make seven annual payments of K to repay the loan, with the first payment made three years from the date of renegotiation. (ii) The interest rate is changed from 7.5% effective annually. Calculate K (do not use excel)

(A) 11,068 (B) 11,666 (C) 11,900 (D) 12,193 (E) 12,540

Answer 1

Answer is (D) = 12,540

Calculation is given below

1st Step - Calculate Original Annual Payment (Here payment is made at end of the year)

Formula - {P * R * (1+R)^N} / { (1+R)^N - 1}

P = Principal Amount (1,00,000)

R = Annual Interest Rate (6%)

N = Loan Tenure (15 Years)

Using the above formula we get Original Annual EMI = 10,296

The following will be repayment schedule

Evident from abive table, now after 8th payment pending payable principal is 57,478 (Rounded Off)

Now post renegotiation borrower will make 7 annual payments starting 3 years from now, new interest rate will be 7.5%

Pending after 3 years (which will be repaid in 7 annual payments of amount K)

= 57,478 (1.075)^3

= 71,405

Now 7 annual payments (Of Amount K) will be made at the beginning of each year

Amount (K) of which will be calculated using formula used abive for calculating original annual payment with a slight modification since here payments are made at the beginning of the year

Formula will be

K = { (P - K) * R * (1+ R)^(N-1) } / { (1 + R) ^ (N - 1) - 1 }

It will be solved as below giving K = 12,540