Question

20. Assume that your father is now so years old, that he plans to retire in 10 years, and that he expects to live for 25 years after he retires (that is, until he is 85). If he retired today, he could live comfortably on $50,000 per year. However, because of inflation, his target retirement income must increase by 5% per year until his retirement date (.e. inflation is 5% annually). In other words, he must receive more than $50,000 per year upon retirement to have the same purchasing power that $50,000 would provide today For the sake of simplicity, assume that his retirement payment will remain level after he retires.. His will begin drawing from his retirement account the day he retires (.e., 10 years from todav), and then will mal he retires (i.e., 10 years from today), and then will make 25 withdrawals in all. He currently has $50,000 saved up and he expects to earn a return on his savings of 8 percent per year. To the nearest dollar, how much must he save during each of the next 10 years (with deposits being made at the beginning of each year) in order to meet his retirement goal?

Answer 1

First, we calculate the yearly withdrawal required during retirement.

Yearly withdrawal = income required in today's dollars * (1 + inflation rate)^{years until retirement}

Yearly withdrawal = $50,000 * (1 + 5%)¹⁰ = $81,444.73

Now, we calculate the amount required at retirement to enable the required withdrawals during retirement.

Amount required at retirement is calculated using PV function in Excel :

rate = 8% (rate of return on savings)

nper = 25 (number of years in retirement)

pmt = -81444.73 (Yearly withdrawal required during retirement. This is entered with a negative sign because it is a withdrawal)

fv = 0 (amount remaining after 25 withdrawals is zero)

type = 1 (each withdrawal made at the beginning of the year - annuity due)

PV is calculated to be $938,956.61

* - A 1 $938,956.61 f C =PV(8%,25,-81444.73,0,1) D E B

Now, we calculate the yearly saving required to accumulate the required amount in 10 years :

Yearly saving required is calculated using PMT function in Excel :

rate = 8% (rate of return on savings)

nper = 10 (number of years until retirement)

pv = 50000 (Amount already saved now)

fv = 938956.61 (amount required in 10 years)

type = 1 (each saving is made at the beginning of the year - annuity due)

PMT is calculated to be $66,914.05

А2 : х v f =PMT(8%,10,50000, А1,1) B C D E F A 1 $938,956.61 2 | ($66,914.05)

He must save $66,914.05 each year to meet retirement goal.