after retiring, delia wants to be able to withdraw $8,500.00 every quarter from her account for 33 years…

after retiring, delia wants to be able to withdraw $8,500.00 every quarter from her account for 33 years. her account earns 6% interest compounded quarterly. how much does delia need in her account when she retires? delia needs in her account when she retires. how much total money will delia pull out of her account? in total, delia will pull out from her account. hint how much of that money is interest? the amount of money that is interest is . hint

after retiring, delia wants to be able to withdraw $8,500.00 every quarter from her account for 33 years. her account earns 6% interest compounded quarterly. how much does delia need in her account when she retires? delia needs in her account when she retires. how much total money will delia pull out of her account? in total, delia will pull out from her account. hint how much of that money is interest? the amount of money that is interest is . hint

Answer

Explanation:

Step1: Calculate the number of periods

The number of years is $n = 33$ and since withdrawals are quarterly, the number of periods $t=33\times4 = 132$. The quarterly - interest rate $r=\frac{6%}{4}=0.015$, and the quarterly withdrawal amount $P = 8500$.

Step2: Use the present - value of an ordinary annuity formula

The formula for the present value of an ordinary annuity is $PV = P\times\frac{1-(1 + r)^{-t}}{r}$. Substitute $P = 8500$, $r=0.015$, and $t = 132$ into the formula. [ \begin{align*} PV&=8500\times\frac{1-(1 + 0.015)^{-132}}{0.015}\ &=8500\times\frac{1 - 1.015^{-132}}{0.015} \end{align*} ] Using a calculator, $1.015^{-132}\approx0.1407$. Then $1-1.015^{-132}=1 - 0.1407 = 0.8593$. And $\frac{0.8593}{0.015}\approx57.2867$. So $PV=8500\times57.2867 = 487936.95$.

Step3: Calculate the total amount withdrawn

The total amount withdrawn $A_{total}$ is the amount of each withdrawal times the number of withdrawals. So $A_{total}=8500\times132=1122000$.

Step4: Calculate the interest amount

The interest amount $I$ is the total amount withdrawn minus the present value of the annuity. So $I=1122000 - 487936.95=634063.05$.

Answer:

Delia needs $487936.95$ in her account when she retires. In total, Delia will pull out $1122000$ from her account. The amount of money that is interest is $634063.05$.