The National Science Foundation (NSF) offers grants to students who are interested in pursuing a college education. The student must be enrolled full time ( 12 credit hours or more), and hold a grade point average of 3 point 8 The NSF will pay 9 dollars comma 500 per year towards tuition for 4 years. The initial amount is placed into an account paying 7 point 8 percent compounded annually, and the tuition is drawn from the account until the remaining balance is zero dollars. Determine the initial amount invested by the NSF. Round your answer to the nearest dollar.
Treat the four yearly tuition payments of $9,500 as withdrawals at the end of each year. The initial deposit must equal their present value: $9,500 × [1 − (1.078)⁻⁴] ÷ 0.078 ≈ $31,606. Rounded to the nearest dollar, the initial amount is $31,606, choice C.
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