Answer to Question #261759 in Financial Math for Katie

Question #261759

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 If the early withdrawal penalty is 10% of the amount withdrawn, how much will she have to pay?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


1
Expert's answer
2021-11-18T17:44:30-0500

a)

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 (decimal)
  • 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, 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"


b)

Future value, F"= 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"






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