5
QuizMultiple Choice

Credit and Types of Loans — Test

Question 5 • Financial Math

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.

Answer
A
55 dollars comma 200
B
52 dollars comma 000
C
60 dollars comma 886
D
64 dollars comma 235

Explanation

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.

AI-written and checked against the verified answer.

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