Answer to Question #266518 in Financial Math for Jack

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 If the early withdrawal penalty is 10% of the amount withdrawn, how much will she have to pay?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. $1,003.59 b. $40,143.57 c. $4,014.36 d. $10,035.89

Sergio plans to retire in 15 years. He would like to have $250,000 in his retirement account. If he invests in a plan that pays 4.69% interest compounded monthly, how much should he contribute monthly?

a. $138.89 b. $277.88 c. $959.77 d. $560.23

Answer 1

a)$Total Payments = A\times nper$

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

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

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

$nper = p \times t$

Where;

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

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

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

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

Sarah will have to pay $1003.59 to withdraw $25\%$ of the money from her account.

b)

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

$250000= A\times\frac{(1+0.0039)^{180 }- 1}{0.0039}$

$250000= 260.47A$

$\therefore A=\$959.77$

Sergio will contribute $959.77 monthly in order to have $\$250,000$ in his retirement account after 15 years.