A $3000 loan is to be repaid with quarterly payments or $R over five years,1^st payment due 3 months from now.What is R if j₂ = 10%?

Question

Quizplus · Accepted Answer

The loan repayment can be calculated using the formula for the present value of an annuity: $PV = R \times \frac{1 - (1 + i)^{-n}}{i}$, where $PV$ is the present value (loan amount), $R$ is the regular payment, $i$ is the interest rate per period, and $n$ is the total number of payments. Given a semi-annual interest rate of 10%, the quarterly interest rate is $10\%/4 = 2.5\%$, or $0.025$ in decimal form. The total number of quarterly payments over five years is $5 \times 4 = 20$. Plugging these values into the formula gives $3000 = R \times \frac{1 - (1 + 0.025)^{-20}}{0.025}$. Solving for $R$ gives approximately $191.89.

A $3000 Loan Is to Be Repaid with Quarterly Payments