Answer to Question #254779 in Financial Math for Katie

Question

Sarah had been contributing $300 pre-tax per month to a retirement account that pays 2.16% interest compounded monthly. After 10 years, she needs to withdraw 25% of the money from her account. If the early withdrawal penalty is 10% of the amount withdrawn, how much will she have to pay? A. $1003.59 B. $40,143.57 C. 4,014.36 D. 10,035.89

Answer 1

Solution:

Total payments=$\$300\times12\times10=\$36,000$

Future value, F$= A\times\frac{(1+rate)^{nper }- 1}{rate }$

$rate = (1+\frac{r}{n})^{\frac{n}{p}}-1$

$n\ per = p \times t$

Where;

• r = nominal annual interest rate (decimal)
• n = number of compounding periods per year
• p = number of payment periods per year
• rate = rate per payment period
• n per = total number of payment periods
• A = an amount added to the principal at the end of each payment period

Future value, F$= 300\times\frac{(1.0018)^{120 }- 1}{0.0018}=40143.57$

Withdrawing $25\%$ and incurring a $10\%$ withdrawal fee, she will pay:

$0.25\times0.1\times40143.5=\$1003.59$

So, option A. is correct.