Answer to Question #268281 in Financial Math for Shay

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 If the early withdrawal penalty is 10% of the amount withdrawn, how much will she have to pay?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

1.

The penalty amount will be applicable on the future value amount after 10 years

$Future \space value = Deposit×((1+Rate)^N−1)\div Rate\\where \\Rate = \frac{2.16\%}{12} = 0.18\%\\and \\N = 10 ×2 = 120 \space months\\FV = \$300×((1+0.18\%)120−1)\div 0.18\%\\= \$300×133.8119007\\= \$40,143.57\\Penalty\space amount = Future \space value×Withdrawal \%×Penalty\%\\= \$40,143.57×25\%×10\%\\= \$1,003.59$

Penalty amount = $1,003.59

Correct choice A

2.

Since the interest is compounded monthly, we should compute the effective interest rate.