1. **State the problem:** Find the future value of an ordinary annuity with payment $650$, interest rate $1.45\%$ compounded semiannually, over 6 years. 2. **Formula for future value of an ordinary annuity:** $$FV = PMT \times \frac{(1 + r)^n - 1}{r}$$ where: - $PMT$ is the payment per period, - $r$ is the interest rate per compounding period, - $n$ is the total number of compounding periods. 3. **Calculate the interest rate per period and number of periods:** - Annual interest rate = $1.45\% = 0.0145$ - Compounded semiannually means 2 periods per year. - Interest rate per period: $$r = \frac{0.0145}{2} = 0.00725$$ - Number of periods: $$n = 6 \times 2 = 12$$ 4. **Substitute values into the formula:** $$FV = 650 \times \frac{(1 + 0.00725)^{12} - 1}{0.00725}$$ 5. **Calculate $(1 + 0.00725)^{12}$:** $$1.00725^{12} \approx 1.0891$$ 6. **Calculate numerator:** $$1.0891 - 1 = 0.0891$$ 7. **Calculate fraction:** $$\frac{0.0891}{0.00725} \approx 12.2966$$ 8. **Calculate future value:** $$FV = 650 \times 12.2966 = 7993.79$$ **Final answer:** The future value of the ordinary annuity is approximately **7993.79**.