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In: Finance

Assume you are 25 and earn ​$31,000 per​ year, never expect to receive a​ raise, and...

Assume you are 25 and earn ​$31,000 per​ year, never expect to receive a​ raise, and plan to retire at age 55. If you invest 5 percent of your salary in a​ 401(k) plan returning 11 percent​ annually, and the company provides a​ $0.50 per​ $1.00 match on your contributions up to 3 percent of​ salary, what is the estimated future value of your​ 401(k) account? Once you​ retire, how much can you withdraw monthly if you want to deplete your account over 30 ​years? 

Solutions

Expert Solution

  • You contribute 5% of your salary and employer contributes half of that so he contributes 2.5%
  • So total contribution that goes each year = 7.5% x 31000 = $2325
  • With this information, we need to find the FV of the annuity:
    • We are given the following information
    • PMT 2325
      r 11.00%
      n 30
      T 1
    • We need to solve the following equation to arrive at the required FV
    • So the FV is $462723.54
  • So at the time of retirement we will have the quantum of  $462723.54
    • We need to find the annual PMT from this for 30 years of retired life
    • We are given the following information:
    • r 11.00%
      n 30
      frequency 1
      PV $        4,62,723.54
    • We need to solve the following equation to arrive at the required PMT
    • So the annual withdrawal can be of $53,224.59 for the funds to last for 30 years and completely deplete at the end of this period

jeff jeffy answered 1 hour ago
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