1. **State the problem:** Peter deposits 480 on January 3 in a savings account paying 3.5% annual interest compounded quarterly on January 2, April 1, July 1, and October 1. We want to find the balance after 9 months. 2. **Identify the compounding periods:** Interest is added quarterly, so the interest rate per quarter is $ \frac{3.5}{4} = 0.875\% $ per quarter. 3. **Determine the number of quarters in 9 months:** 9 months = 3 quarters. 4. **Use the compound interest formula:** $$ A = P \left(1 + \frac{r}{n}\right)^{nt} $$ where: - $P = 480$ (principal), - $r = 0.035$ (annual interest rate), - $n = 4$ (compounding periods per year), - $t = \frac{9}{12} = 0.75$ years. 5. **Calculate the amount:** $$ A = 480 \left(1 + \frac{0.035}{4}\right)^{4 \times 0.75} = 480 \left(1 + 0.00875\right)^3 = 480 \times 1.00875^3 $$ 6. **Calculate $1.00875^3$:** $$ 1.00875^3 = 1.00875 \times 1.00875 \times 1.00875 = 1.0265 \text{ (approx)} $$ 7. **Calculate final balance:** $$ A = 480 \times 1.0265 = 492.72 \text{ (approx)} $$ **Final answer:** After 9 months, Peter's balance should be approximately **492.72**.