Question 5 Notyetanswered Points out of 10.00 p Flag question Jon wishes to accumulate \( \$ 4,500 \) in 8 years for a long vacation. Use Table \( 12-1 \) to find the sinking fund payment he would need to make at the END of every six months, at \( 4 \% \) interest compounded semiannually. Select one: a. \( \$ 241,43 \) b. \( \$ 233.97 \) c. \( \$ 207.63 \) d. \( \$ 344.10 \)

Let the sinking fund accumulation factor for a level payment at the end of each period be \[ a_{\overline{n}\,|\,i} = \frac{(1+i)^{n} - 1}{i} \] where \( i \) is the interest rate per period and \( n \) is the total number of periods. Since the interest rate is \( 4\% \) compounded semiannually, the interest rate per six-month period is \[ i = \frac{0.04}{2} = 0.02 \] and the number of six-month periods in 8 years is \[ n = 8 \times 2 = 16. \] The sinking fund equation is \[ \text{Payment} \times a_{\overline{16}\,|\,0.02} = \$4500. \] First, compute the accumulation factor: \[ a_{\overline{16}\,|\,0.02} = \frac{(1.02)^{16} - 1}{0.02}. \] Approximating \((1.02)^{16}\): \[ (1.02)^{16} \approx 1.373 \] thus \[ a_{\overline{16}\,|\,0.02} \approx \frac{1.373 - 1}{0.02} = \frac{0.373}{0.02} \approx 18.65. \] Now, solve for the sinking fund payment: \[ \text{Payment} = \frac{4500}{18.65} \approx 241.43. \] Therefore, the required sinking fund payment is approximately \( \$241.43 \). The correct answer is: a. \( \$241.43 \)