A.) In order to sustain the post-tax standard of living throughout retirement (n

Question

A.) In order to sustain the post-tax standard of living throughout retirement (not just for first year), how much money would you need at the beginning of your first year of retirement (in that year's dollars)?

B.) What is the present value of the amount in (a)?

C.) Assuming you save the same dollar amount in each of the 25 years before retirement,

always making contributions at the end of each year (including the 25th year), how much

would you need to save (per year) in order to reach the retirement portfolio value computed

in part (a)?

D.) Assuming your contributions grow at 3% per year, and always making contributions at

the end of each year (including the 25th year), how big would your first contribution (one

year from now) need to be in order to reach the portfolio value computed in part (a)?

Inflation Standard of living (present value) Tax rate during retirement Years until retirement Return on investments, pre-retirement Return on investments, post-retirement All retirement spending is at end of year You will live forever (for simplicity) 2% 125,000 per year after tax 20% 25 10% 6%

Explanation / Answer

A. The posttax amount required today= 125,000

The pretax amount would be 125,000/(1-0.2) = 156,250 considering 20% tax

The requirement in the first year of retirement 25 years from today accounting for inflation = 156,250*1.02^25 = 256,344.69

The will be the Cash requirement for year 1

Present value = C/(r-g) where r = 0.06 and g = 0.02 (inflation) = 256,344.69/(0.06-0.02) = 6,408,617.17

Total money required beginning of your retirement = $6,408,617.17

B. Present value of this amount considering pre-retirement rate of 10% =6,408,617.17/1.10^25 = $591,489.72

C. Amount of money to save per year = PMT(rate,nper,pv,fv) in excel where FV =6,408,617.17, nper = 25 and rate 0.10

Amount of money to save per year =PMT(0.10,25,0,6408617.17) = $65,163.68

D. Now, we will have a growing annuity at 3%. the FV of whichis known

FV of a growing annuity = P*((1+r)^n -(1+g)^n)/(r-g)

6408617.17 = P*(1.10^25-1.03^25)/(0.10-0.03)

P = 51,322.15

First contribution =$51,322.15

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