Question

Alex would like to accumulate $1,000,000 to cover life expenses during retirement. Alex expects to retire in 30 years, and expects to live for 20 years thereafter. Inflation over the next 30 years is expected to average 2% per year, and the average rate of return on pre-retirement aggressive investments over the next 30 years is 15%. After 30 years, the average rate of return on more conservative post-retirement investments is 7%.

1. Calculate the present value amount that Alex would need to deposit today to meet the goal of accumulating $1,000,000 adjusted for inflation (5 points). Use a time line to illustrate the problem (5 points).
2. Calculate the annual withdrawal amount that Alex will need to make on an annual basis while on retirement to use up his retirement savings over 20 years (5 points). Use a timeline to illustrate the problem (5 points). Assume that withdrawals are made at the end of each year.

Answer 1

Alex would like to accumulated 1,000,000 $ to cover life expense during retirement. Alex espects to retire in 30 years and expects to live for 20 years thereafter. We have drawn this in the time line below

t = 0   t = 30 t= 50

(Present) (Retirement)   (Death)

Retirement Saving at t = 20 is 1,000,000 $

Inflation over the next 30 years expected to be 2% and average rate of return on pre retirement saving is 15 %

So his pre retirement saving is going to fetch a real rate of return of 15 - 2 = 13 %

After 30 years his planned post retirement savings is going to give a return on 7%

a) Now let us calculate how much he needs to deposit today to get his retirement saving at t = 30

FV = 1,000,000 $ , n = 30 , r = 13 % and we need to calculate PV at t = 0

PV = FV/ {(1+r) ^ n} = 1,000,000/{(1+.13)^30} = 1,000,000/39.11 = 25,569 $

So Alex needs to deposit 25,569 $ now to achieve his retirement goal.

b) Alex wants to consume his retirement saving of 1,000,000 at retirement for next 20 years through annnual withdrawal

So in this case PV will be his saving at retirement 1,000,000 $ , FV = 0 , n = 20 , r = & % and we want to calculate PMT

Putting this into the exce formula = PMT(.07,20,1,000,000,0) = 94,393 $

So Alex needs to draw 94,393 $ annually to exhaust his retirement savings.