Sally Has A Retirement Question

Problem:

Sally is 30 years old and has an annual salary of $72,000. She wants to retire at 60. She expects to live up to 80 years and would like to draw $4000 per month ($48,000 per year) from her tax deferred 401k account after her sixtieth birthday.

When she is working, assume her investment is growing at the rate of 8%. When she is retired, the market interest rate is at 4% for the next 20 years.

Assume all compounding is done on a monthly basis during her investment period and retirement period. She currently does not have any money in her 401k account.

You are a close friend of hers and she asks you the following questions:

(1) How much should she have in her tax deferred account (401k) when she is 60 years old?

  • (A) $1,000,000
  • (B) $737,684
  • (C) $559,655
  • (D) $660,087

(2) How much should she put in her tax deferred account (401k) on a monthly basis to achieve the nest egg amount above?

  • (A) $875
  • (B) $443
  • (C) $375
  • (D) $667

Answers:

  • Question 1 = $660,087
  • Question 2 = $443

Explanation:

Prerequisite for understanding and solving this problem is: Time Value of Money

Any financial scenario is best understood with a timeline. So, let us draw the timeline and put down everything defined in the problem:

Retirement_x1a

We know the market interest interest rate is 4% for 20 years from when Sally is 60 to 80 years of age.  We also know that she will drawing $4000 per month  over a 20 year (240 month period).

Hence, we can travel the timeline, as shown by the green arrow with the information we have on hand and calculate how much she will need in her nest egg.

Retirement_x2a

In Excel, type “=PV(0.04/12, 12*20, 4000)”, you will get $660,087.43, rounding off decimals to the nearest integer, you get $660,087.

The next step is to determine how much Sally would need to contribute to her 401k on a monthly basis to achieve $660,087. We know her investment would grow at the rate of 8% compounded on a monthly basis. Hence, we can travel the timeline, as shown by the green arrow with the information we have on hand and calculate how much she will need to invest on a monthly basis to achieve her nest egg.

Retirement_x3a

In an Excel cell, type “=PMT(0.08/12, 12*30,0,-660087.43)“, you will get $442.90, rounding off decimals to the nearest integer, you get $443.

 

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