Question

  Joan Messineo borrowed 42,000 at a 5​% annual rate of interest to be repaid over 3 years. The loan is amortized into three​ equal, annual,​ end-of-year payments.

a.  Calculate the​ annual, end-of-year loan payment.

b.  Prepare a loan amortization schedule showing the interest and principal breakdown of each of the three loan payments.

c. Explain why the interest portion of each payment declines with the passage of time.

Answer 1

a) We would use the baisc time value of money function, concept about annuities to calculate this. PV of an ordinary annuity is mathematically represented as:

42,000 = P * 2.7232

P = $15,422.76 ----> Equal annual payment to be made

b)

c) Interest portion of the monthly payment is calculated by application of interest rate on the principal component outstanding at end of the year. Now, since the monthly payment contains two components - interest and principle repayment, principal repayment reduced the amount of outstanding (or ending) principle which would reduce the interest rate amount for next year.

However, the payment to payback loan remains same every year. In order to balance out the reduced payment of interest as we move towards loan maturity, principal repayment component increases (which further leads to decline in interest component as we move ahead).