1. **State the problem:** We have a principal amount $P = 7500$ deposited at an interest rate of 6.5% per year compounded quarterly for 25 years. We need to find the accumulated sum. 2. **Formula used:** The formula for compound interest is: $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where: - $A$ is the accumulated amount (principal + interest), - $P$ is the principal amount, - $r$ is the annual interest rate (decimal), - $n$ is the number of times interest is compounded per year, - $t$ is the time in years. 3. **Identify values:** - $P = 7500$ - $r = 6.5\% = 0.065$ - $n = 4$ (quarterly compounding) - $t = 25$ 4. **Substitute values into the formula:** $$A = 7500 \left(1 + \frac{0.065}{4}\right)^{4 \times 25}$$ 5. **Simplify inside the parentheses:** $$1 + \frac{0.065}{4} = 1 + 0.01625 = 1.01625$$ 6. **Calculate the exponent:** $$4 \times 25 = 100$$ 7. **Calculate the accumulated amount:** $$A = 7500 \times (1.01625)^{100}$$ 8. **Calculate the power:** Using a calculator, $$(1.01625)^{100} \approx 4.724$$ 9. **Multiply to find $A$:** $$A = 7500 \times 4.724 = 35430$$ 10. **Final answer:** The accumulated sum after 25 years is approximately **35430**.