Question

question 4
after retiring, shanice wants to be able to withdraw $32,500.00 every year from her account for 27 years. her account earns 7% interest compounded annually.
how much does shanice need in her account when she retires?
shanice needs in her account when she retires.
how much total money will shanice pull out of her account?
in total, shanice will pull out from her account. hint
how much of that money is interest?
the amount of money that is interest is . hint
question help: video 1 video 2

Explanation:

Step1: Identify the type of problem

This is a present value of an ordinary annuity problem. The formula for the present value (PV) of an ordinary annuity is $PV = PMT \times \frac{1 - (1 + r)^{-n}}{r}$, where $PMT$ is the payment per period, $r$ is the interest rate per period, and $n$ is the number of periods.

Step2: Extract the given values

• $PMT = \$32,500$ (annual withdrawal)
• $r = 7\% = 0.07$ (annual interest rate)
• $n = 27$ (number of years)

Step3: Calculate the present value (amount needed at retirement)

Substitute the values into the formula:

$$
LATEXBLOCK0
$$

First, calculate $1.07^{-27}$. Using a calculator, $1.07^{-27} \approx 0.17843087$. Then, $1 - 0.17843087 = 0.82156913$. Now, divide by $0.07$: $\frac{0.82156913}{0.07} \approx 11.7367019$. Multiply by $32500$: $32500 \times 11.7367019 \approx 381,442.81$.

Step4: Calculate total money pulled out

Total money pulled out is simply the annual withdrawal times the number of years: $32500 \times 27 = 877,500$.

Step5: Calculate the interest

Interest is total money pulled out minus the present value: $877500 - 381442.81 = 496,057.19$.

Answer:

• Amount needed at retirement: $\$381,442.81$
• Total money pulled out: $\$877,500$
• Interest: $\$496,057.19$