A loan is being repaid by 20 equal semi-annual installments.The principal portion of the 8^th payment is $245.29 and the interest portion is $254.71.What interest rate,j₂ is being charged on the loan?

Question

Quizplus · Accepted Answer

Since the loan is being repaid by 20 equal semi-annual installments, there are a total of 40 payments. Let P be the principal amount of the loan and r be the interest rate per period. Then we have:

- Each semi-annual payment is P/20 + Pr/2.
- The principal portion of the 81st payment is P/20.
- The interest portion of the 81st payment is Pr/2.

We are given that the principal portion of the 81st payment is $245.29 and the interest portion is $254.71. Therefore:

- P/20 = $245.29
- Pr/2 = $254.71

Solving for P and r, we get:

- P = $4,905.80
- r = 0.055 or 5.5% per semi-annual period

The annual interest rate is twice the semi-annual rate, so the answer is:

- j = 2r = 0.11 or 11%

Therefore, the best choice is B.

A Loan Is Being Repaid by 20 Equal Semi-Annual Installments