You are 30 years old and want to retire at 55. However, you do not want to start
ID: 2720882 • Letter: Y
Question
You are 30 years old and want to retire at 55. However, you do not want to start withdrawing your retirement accounts and social security until 62.You must, therefore, fund 7 years' worth of living expenses and you estimate you'll need $5,850/month during that period. If you earn 3.20% on any money invested in non-retirement accounts during the 55-62 time period and can earn 6.15% annually on your investments prior to age 55, how much must you invest at the end of each month starting next month to fund your early retirement?Explanation / Answer
Answer: $1374
Amount to be had in the fund at the beginning of the 55th year = the pv of monthly annuity of $5850 discounted at 3.2% p.a.
PV of the annuity = 5850*pvifa(3.2/12,84) = 5850*75.164 = $439,709.4
This amount is the FV of the annuity that is to be invested each month for the years 30 to 55, ie: for 25 years
So. $439,709.4 = A*fvifa(6.15/12,300)
439709.4 = A*319.9937
A = $1374.12 rounded off to $1374
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