Find the amount necessary to fund the given withdrawals. Semiannual withdrawals of \( \$ 650 \) for 9 years; interest rate is \( 6.1 \% \) compounded semiannually. The amount necessary to fund the given withdrawals is \( \$ \square \) (Round to the nearest cent as needed.)

To find the amount necessary to fund the semiannual withdrawals of \( \$ 650 \) for 9 years at an interest rate of \( 6.1\% \) compounded semiannually, we can use the formula for the present value of an annuity. The formula is: \[ PV = P \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \] Where: - \( P \) is the payment amount (\$650), - \( r \) is the interest rate per period (which is \( 0.061/2 = 0.0305 \)), - \( n \) is the total number of payments (which is \( 9 \times 2 = 18 \)). Calculating each component: - \( r = 0.0305 \) - \( n = 18 \) Now plug in the values: \[ PV = 650 \times \left( \frac{1 - (1 + 0.0305)^{-18}}{0.0305} \right) \] Calculating \( (1 + 0.0305)^{-18} \): \[ (1.0305)^{-18} \approx 0.5263 \] Now substitute back into the formula: \[ PV = 650 \times \left( \frac{1 - 0.5263}{0.0305} \right) \] \[ = 650 \times \left( \frac{0.4737}{0.0305} \right) \] \[ \approx 650 \times 15.5 \] \[ \approx 10007.50 \] Therefore, the amount necessary to fund the given withdrawals is approximately \( \$ 10007.50 \).