1. **State the problem:** We need to find the future value of an ordinary annuity with the following details: - Periodic payment: 4100 - Payment interval: 1 year - Term: 10 years - Interest rate: 10% per year - Conversion period: semi-annually 2. **Formula for future value of an ordinary annuity:** $$FV = P \times \frac{(1 + r)^n - 1}{r}$$ where: - $P$ is the periodic payment - $r$ is the interest rate per payment period - $n$ is the total number of payments 3. **Adjust the interest rate and number of periods:** Since the interest is compounded semi-annually but payments are yearly, we must adjust the rate and periods accordingly. - Number of compounding periods per year = 2 - Interest rate per compounding period = $\frac{10\%}{2} = 0.05$ - Total compounding periods = $10 \times 2 = 20$ 4. **Calculate the effective annual interest rate:** $$r_{effective} = (1 + 0.05)^2 - 1 = 1.1025 - 1 = 0.1025$$ 5. **Use the effective annual rate for the annuity since payments are yearly:** - $P = 4100$ - $r = 0.1025$ - $n = 10$ 6. **Calculate the future value:** $$FV = 4100 \times \frac{(1 + 0.1025)^{10} - 1}{0.1025}$$ 7. **Calculate $(1 + 0.1025)^{10}$:** $$1.1025^{10} = 2.653298$$ (rounded to six decimal places) 8. **Calculate numerator:** $$2.653298 - 1 = 1.653298$$ 9. **Calculate fraction:** $$\frac{1.653298}{0.1025} = 16.132390$$ 10. **Calculate future value:** $$FV = 4100 \times 16.132390 = 66142.799$$ 11. **Round to nearest cent:** $$FV = 66142.80$$ **Final answer:** The future value of the ordinary annuity is **66142.80**.