Question

Your company is planning to borrow $1 million on a 3-year, 12%, annual payment, fully amortized term loan. What fraction of the payment made at the end of the second year will represent repayment of principal? Round your answer to two decimal places. ________ %

Answer 1

Borrowing = $ 1000000, Tenure = 3 years, Interest Rate = 12 %

Let the equal annual repayment be $ P

1000000 = P x (1/0.12) x [1-{1/(1.12)^(3)}]

1000000 = P x 2.401831

P = 1000000 / 2.401831 = $ 416348.98 ~ $ 416349

At the end of Year 1:

Interest Accrued = 1000000 x 0.12 = $ 120000, Annual Payment = $ 416349

Principal Repaid = 416349 - 120000 = $ 296349

Principal Outstanding = 1000000 - 296349 = $ 703651

At the end of Year 2:

Interest Accrued = 703651 x 0.12 = $ 84438.12, Annual Payment = $ 416349

Principal Repaid = 416349 - 84438.12 = $ 331910.88

Principal Outstanding = 703651 - 331910.88 = $ 371740.12

Principal Repaid as Fraction of Annual Repayment = (331910.88 / 416349) = 0.79719 or 79.719 % ~ 79.72 %