1. **State the problem:** Calculate the quarterly payment for a $12000 motorcycle loan over 5 years at an annual interest rate of 7.2%, with payments made quarterly. 2. **Formula used:** The payment for an installment loan with compound interest and regular payments is given by the amortization formula: $$ P = \frac{r \times PV}{1 - (1 + r)^{-n}} $$ where: - $P$ is the payment per period, - $PV$ is the present value or loan amount, - $r$ is the interest rate per period, - $n$ is the total number of payments. 3. **Identify variables:** - Loan amount $PV = 12000$ - Annual interest rate = 7.2% = 0.072 - Number of years = 5 - Payments per year = 4 (quarterly) 4. **Calculate interest rate per period:** $$ r = \frac{0.072}{4} = 0.018 $$ 5. **Calculate total number of payments:** $$ n = 5 \times 4 = 20 $$ 6. **Substitute values into the formula:** $$ P = \frac{0.018 \times 12000}{1 - (1 + 0.018)^{-20}} $$ 7. **Calculate denominator:** $$ 1 + 0.018 = 1.018 $$ $$ (1.018)^{-20} = \frac{1}{(1.018)^{20}} \approx \frac{1}{1.432364} \approx 0.6985 $$ $$ 1 - 0.6985 = 0.3015 $$ 8. **Calculate numerator:** $$ 0.018 \times 12000 = 216 $$ 9. **Calculate payment:** $$ P = \frac{216}{0.3015} \approx 716.68 $$ **Final answer:** The quarterly payment is approximately $716.68.