Assume that you are presently 30 years old and that you intend to retire when yo
ID: 2777878 • Letter: A
Question
Assume that you are presently 30 years old and that you intend to retire when you turn 65. You would like to make sure that you have enough funds at the point of retirement to last until you are 95. You estimate that it would take $72,000 per year, in today’s dollars to maintain a lifestyle that you desire.
Assume inflation is 2.8% and that you can get a 10% return on your long term investments until you retire. You also estimate that you should be able to get 6% secure returns on your investment after you retire.
How much should you be setting aside yearly between now and your retirement to meet your goals?
What happens if you decide to wait an additional 15 years before starting to save for retirement? How much would you have to set aside?
Assuming that you start saving at 35, what would happen if you decide to retire early?
Please show all work.
Explanation / Answer
The cash flow required in 35 years when you turn 65 is $72,000 per year for whole span of 30 years of retirement in today’s dollars .The inflation adjusted cash flow required at t=65 at point of retirement=72,000*(1.028)35,at t=66 =72,000*(1.028)36 ,.......at t=94= 72,000*(1.028)64 Present value of $above cash flows for whole span of 30 years of retirement at time of retirement=B=72,000*(1.028)35+72,000*(1.028)36/1.06 +.....+ 72,000*(1.028)64/1.0629
=>B=72,000*(1.028)35(1+(1.028/1.06) +.....+ 72,000*(1.028/1.06)29)
(1+(1.028/1.06) +.....+ 72,000*(1.028/1.06)29) is GP with first term =1 and common ratio=cr=1.028/1.06 and no of terms=T=30
Sum of GP= first term*(1-crT)/(1-cr) =(1-(1.028/1.06)30)/(1-1.028/1.06)=0.60132639/0.03018867=19.9189
B=72,000*2.6288* 19.9189
B=3770121.91
B=(A/y)[(1+y)T-1] where B=3770121.91, A is annual money u should be setting aside yearly between now and your retirement(set aside money from year when u turn 31 to year when u turn 64) to meet your goal of accumulating 3770121.91 at point of retirement t=65,y=.10,T=35
B=A(1+y)T-1+ A(1+y)T-2+........+A(1+y) = A(1+y) +.....+A(1+y)T-1 = A(1+y) *((1+y)T-1-1)/(1+y-1)=(A/y)(1+y) *((1+y)T-1-1)
A=(B*y/(1+y))/[(1+y)T-1-1]=(3770121.91*.1/1.1)/[(1.1)34-1]=342738.355/24.548=$13961.97
Thus $13961.97 should you be setting aside yearly between now and your retirement to meet your goals.
when you wait for additional 15 years,
T=35-15=20
A=(B*y/(1+y))/[(1+y)T-1-1]=(3770121.91*.10/1.1)/[(1.1)19-1]=342738.36/5.1159=$66994.73
Thus $66994.73 should you be setting aside yearly between now and your retirement to meet your goals.
If you start saving at 35 then T=35-5=30,total money i accumulate at 10% till retirement=B=(A/y)*(1+y)*[(1+y)T-1-1]= (13961.97/.1)*(1.1)(1.129-1) =$2282698.64 which shall fall short of the required amount of $3770121.91 and if you decide to retire early then also there will be short fall of funds to fund the retirement because now more sum is required to meet retirement goals.