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. \( \$ 344.10 \)
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To determine the correct sinking fund payment Jon needs to make, we first need to find the future value interest factor for an annuity at the given rate and time. With 4% interest compounded semiannually, the effective rate per period is 2%. Over 8 years, with payments made every six months, Jon will make a total of 16 payments. The future value factor for an ordinary annuity can be found using the formula: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] Rearranging gives us the payment \( P \): \[ P = \frac{FV \times r}{(1 + r)^n - 1} \] Substituting the values \( FV = 4500 \), \( r = 0.02 \), \( n = 16 \): \[ P = \frac{4500 \times 0.02}{(1 + 0.02)^{16} - 1} \] Calculating, we find \( P \approx 233.97 \). Thus, the correct answer is b. \( \$ 233.97 \).
