Gabby has $70,000 deposited in an account earning 2.5% interest annually. She plans to withdraw a certain amount from this account at the start of each semi-annual period over 5 years and still have $15,000 remaining. Determine the amount of each payment.

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Quizplus · Accepted Answer

The problem can be solved using the formula for the present value of an annuity due, since Gabby is making withdrawals at the start of each period. The formula is $PV = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right) \times (1 + r)$, where $PV$ is the present value (initial amount minus the remaining amount), $PMT$ is the payment amount, $r$ is the interest rate per period, and $n$ is the total number of periods. Here, $r = 0.025 / 2 = 0.0125$ (since interest is compounded semi-annually), $n = 5 \times 2 = 10$ periods, and $PV = 70000 - 15000 = 55000$. Solving for $PMT$ gives us the correct answer, which matches option A, $5,994.62.

Gabby Has $70,000 Deposited in an Account Earning 2