You are going to withdraw $1,000 at the end of each year for the next three years from an account that pays interest at a rate of 8% compounded annually. The account balance will reduce to zero when the last withdrawal is made. How much interest will you earn on the account over the three year life?

A) $70.00
B) $240.00
C) $422.90
D) $576.24
E) $3,000.00

To solve this, we use the future value of an annuity formula to find the initial amount needed to fulfill these withdrawals. The formula is $FV=P\times \left(\frac{(1+r{)}^n-1}{r}\right)$ , where $FV$ is the future value (which is 0 in this case since the account depletes to zero), $P$ is the payment amount, $r$ is the interest rate per period, and $n$ is the number of periods. However, since we're looking for the initial present value (PV) that can support these withdrawals, we rearrange the formula to solve for PV of an annuity: $PV=P\times \left(\frac{1-(1+r{)}^{-n}}{r}\right)$ . Given $P=\$1,000$ , $r=0.08$ , and $n=3$ , we find the initial amount needed. $PV=\$1,000\times \left(\frac{1-(1+0.08{)}^{-3}}{0.08}\right)=\$1,000\times \left(\frac{1-(1.08{)}^{-3}}{0.08}\right)=\$1,000\times 2.5771=\$2,577.10$ .This is the initial deposit required. Over three years, you withdraw \$3,000 in total (\$1,000 each year for 3 years). The interest earned is the difference between what you withdraw and your initial deposit.Interest earned = Total withdrawals - Initial deposit = \$3,000 - \$2,577.10 = \$422.90.