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.

A) $11,172.50
B) $12,172.50
C) $13,172.50
D) $14,172.50
E) $15,172.50

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.