1. **State the problem:** Find the present value of an ordinary annuity with quarterly deposits of 14481 for 9 years at an interest rate of 4.4% compounded quarterly. 2. **Formula for present value of an ordinary annuity:** $$PV = P \times \frac{1 - (1 + r)^{-n}}{r}$$ where: - $P$ is the payment per period - $r$ is the interest rate per period - $n$ is the total number of payments 3. **Identify values:** - $P = 14481$ - Annual interest rate = 4.4% = 0.044 - Compounded quarterly means 4 periods per year, so $$r = \frac{0.044}{4} = 0.011$$ - Number of years = 9, so total payments: $$n = 9 \times 4 = 36$$ 4. **Calculate present value:** $$PV = 14481 \times \frac{1 - (1 + 0.011)^{-36}}{0.011}$$ 5. Calculate $(1 + 0.011)^{-36}$: $$1 + 0.011 = 1.011$$ $$1.011^{-36} = \frac{1}{1.011^{36}}$$ Calculate $1.011^{36}$: $$1.011^{36} \approx 1.011^{30} \times 1.011^{6}$$ Using a calculator or approximation: $$1.011^{36} \approx 1.432364$$ So: $$1.011^{-36} \approx \frac{1}{1.432364} = 0.6985$$ 6. Substitute back: $$PV = 14481 \times \frac{1 - 0.6985}{0.011} = 14481 \times \frac{0.3015}{0.011}$$ 7. Simplify fraction: $$\frac{0.3015}{0.011} = \frac{\cancel{0.3015}}{\cancel{0.011}} = 27.4091$$ 8. Multiply: $$PV = 14481 \times 27.4091 = 396,737.68$$ **Final answer:** $$\boxed{396737.68}$$ This is the present value of the annuity rounded to the nearest cent.