You plan on withdrawing quarterly payments for the next ten years and have deposited $350,000 in an account. If the rate of return is 5% compounded quarterly, determine the value of the quarterly withdrawals.

Question

Quizplus · Accepted Answer

The value of the quarterly withdrawals can be calculated using the formula for the present value of an annuity: $P = PMT \times \left( \frac{1 - (1 + r)^{-n}}{r} \right)$, where $P$ is the present value ($350,000), $PMT$ is the payment per period (what we're solving for), $r$ is the quarterly interest rate (5% annual rate divided by 4, so 0.0125), and $n$ is the total number of payments (10 years times 4 quarters/year = 40 payments). Rearranging the formula to solve for $PMT$ gives us $PMT = P \times \left( \frac{r}{1 - (1 + r)^{-n}} \right)$. Plugging in the values gives $PMT = 350,000 \times \left( \frac{0.0125}{1 - (1 + 0.0125)^{-40}} \right)$, which calculates to approximately $11,172.50.

You Plan on Withdrawing Quarterly Payments for the Next Ten