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 3.8. The NSF will pay $9,500 per year towards tuition for 4 years. The initial amount is placed into an account paying 7.8% 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 tuition payments as four equal withdrawals made at the end of each year. The initial deposit must equal the present value of those payments: $9,500 × [1 − (1.078)⁻⁴] ÷ 0.078 ≈ $31,606. Therefore, the initial amount is $31,606, choice B.
AI-written and checked against the verified answer.