Emilio is planning a dream vacation and decides to save for it. He chooses a plan with a 3% annual interest rate, compounded semiannually. His goal is to accumulate $10,000 in 7 years. What semiannual deposit amount is required for Emilio to reach his goal of $10,000 in 7 years? Round your answer to the nearest dollar. Periodic deposit future value formula: P=(A((r)/(n)))/((1+(r)/(n))^nt−1)
With semiannual compounding, Emilio makes 2 × 7 = 14 deposits, and the interest rate per period is 0.03 ÷ 2 = 0.015. Substituting into the formula gives P = 10,000(0.015) ÷ [(1.015)^14 − 1] ≈ $647. The required semiannual deposit is therefore $647, choice D.
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