1. **State the problem:** Find the present value of an annuity with payments of 9000 every 6 months for 10 years, with an interest rate of 7% compounded semiannually. 2. **Formula:** The present value $PV$ of an ordinary annuity is given by: $$PV = P \times \frac{1 - (1 + r)^{-n}}{r}$$ where: - $P$ is the payment per period, - $r$ is the interest rate per period, - $n$ is the total number of payments. 3. **Identify values:** - Payment $P = 9000$ - Annual interest rate = 7%, so semiannual rate $r = \frac{7\%}{2} = 0.035$ - Number of years = 10, so total payments $n = 10 \times 2 = 20$ 4. **Calculate:** $$PV = 9000 \times \frac{1 - (1 + 0.035)^{-20}}{0.035}$$ 5. **Evaluate powers:** Calculate $(1 + 0.035)^{-20} = 1.035^{-20} \approx 0.50257$ 6. **Substitute:** $$PV = 9000 \times \frac{1 - 0.50257}{0.035} = 9000 \times \frac{0.49743}{0.035}$$ 7. **Simplify:** $$PV = 9000 \times 14.2123 = 127,910.70$$ **Final answer:** The present value of the annuity is approximately $127,910.70$.