The Academy for Academic Excellence has just announced their winner for the most successful student in mathematics. This student will receive a grant for their college education as well as national recognition for academic excellence in the field of mathematics. The grant will cover 12 dollars comma 177 point 1 7 of the cost of school per year for 5 years. If the initial amount is invested into an account over the five years, paying an annual interest rate of 5 point 5 percent , and you are to withdraw from this account until the remaining balance after the 5 years is zero dollars, determine the initial amount of the grant. Round your answer to the nearest dollar.
Treat the grant as the present value of five equal annual withdrawals of $12,177.17, with each withdrawal made at the end of the year. Use the present-value annuity formula: $12,177.17 × [1 − (1.055)^−5] ÷ 0.055 ≈ $52,000. Therefore, the initial grant is $52,000, choice B.
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