Your company is planning to borrow $1,000,000 on a 5-year,15 percent,annual payment,fully amortized term loan.What fraction of the payment made at the end of the second year will represent repayment of principal?
A) 29.83%
B) 57.18%
C) 35.02%
D) 64.45%
E) 72.36%

Question

Quizplus · Accepted Answer

The total payment for a 5-year, 15 percent, fully amortized term loan can be calculated as follows:

Payment = (Principal x Annual Interest Rate) / (1 - (1 + Annual Interest Rate)-Number of Payments)

Payment = (1,000,000 x 0.15) / (1 - (1 + 0.15)-5)

Payment = $275,252.53

In the first year, the interest portion of the payment is $150,000 (1,000,000 x 0.15) and the principal repayment is $125,252.53 ($275,252.53 - $150,000).

In the second year, the interest portion of the payment is calculated as the outstanding principal balance at the end of year 1, multiplied by the annual interest rate, which is $1,000,000 - $125,252.53 = $874,747.47 x 0.15 = $131,212.12. Therefore, the principal repayment in the second year is $144,040.41 ($275,252.53 - $131,212.12).

The fraction of the payment made at the end of the second year that represents repayment of principal is:

Principal Repayment / Total Payment = $144,040.41 / $275,252.53 = 0.5235

This is equivalent to 52.35%, which is closest to answer choice B (57.18%).

Your Company Is Planning to Borrow $1,000,000 on a 5-Year,15