1. **Problem Statement:** Calculate the accumulated value of periodic deposits of 5500 made at the beginning of every quarter for 7 years, with an interest rate of 3.25% compounded quarterly. 2. **Formula Used:** Since deposits are made at the beginning of each period, we use the future value of an annuity due formula: $$ A = P \times \frac{(1 + r)^n - 1}{r} \times (1 + r) $$ where: - $A$ is the accumulated value - $P$ is the periodic deposit - $r$ is the interest rate per period - $n$ is the total number of deposits 3. **Identify values:** - $P = 5500$ - Annual interest rate = 3.25% = 0.0325 - Compounded quarterly means 4 periods per year, so $r = \frac{0.0325}{4} = 0.008125$ - Number of years = 7, so total periods $n = 7 \times 4 = 28$ 4. **Calculate accumulated value:** $$ A = 5500 \times \frac{(1 + 0.008125)^{28} - 1}{0.008125} \times (1 + 0.008125) $$ 5. **Calculate powers and terms:** $$ (1 + 0.008125)^{28} = 1.008125^{28} \approx 1.2467 $$ 6. **Substitute:** $$ A = 5500 \times \frac{1.2467 - 1}{0.008125} \times 1.008125 = 5500 \times \frac{0.2467}{0.008125} \times 1.008125 $$ 7. **Simplify:** $$ \frac{0.2467}{0.008125} \approx 30.36 $$ 8. **Final multiplication:** $$ A = 5500 \times 30.36 \times 1.008125 \approx 5500 \times 30.61 = 168355.5 $$ 9. **Rounded to nearest cent:** $$ A \approx 168355.50 $$ **Answer:** The accumulated value after 7 years is approximately 168355.50.