Problem

Starting three months after her grandson Robin's birth, MrsDevine made deposits of $110 into a trust fund every three months until Robin was eighteen years old. The trust fund provides for equal withdrawals at the end of each quarter for three years, beginning three months after the last deposit. If interest is 6.8% compounded quarterly how much will Robin receive every three months?

Solution

Step 1 :First, calculate the total number of deposits made by MrsDevine. Robin is 18 years old and the deposits started three months after his birth, so the total number of deposits is \(18 \text{ years} \times 4 \text{ quarters} - 1 \text{ quarter} = 71 \text{ quarters}\).

Step 2 :Next, calculate the future value of these deposits using the formula for the future value of an ordinary annuity: \(FV = P \times [(1 + r/n)^{nt} - 1] / (r/n)\), where P is the amount deposited each period, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years. In this case, P = $110, r = 6.8%, n = 4, and t = 18 years - 3 months = 17.75 years. The future value of the deposits is approximately $14945.07.

Step 3 :After the last deposit, the trust fund will start to make equal withdrawals every quarter for three years. Calculate the present value of these withdrawals using the formula for the present value of an ordinary annuity: \(PV = C \times [1 - (1 + r/n)^{-nt}] / (r/n)\), where C is the amount withdrawn each period. In this case, r = 6.8%, n = 4, and t = 3 years.

Step 4 :Set the future value of the deposits equal to the present value of the withdrawals to find the amount Robin will receive every three months: \(14945.07 = 10.77C\). Solving for C gives the withdrawal amount as approximately $1387.29.

Step 5 :Final Answer: Robin will receive approximately \(\boxed{1387.29}\) dollars every three months.

From Solvely APP
Source: https://solvelyapp.com/problems/25179/

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