A friend of yours wants to start saving for his anticipated retirement and make

Question

A friend of yours wants to start saving for his anticipated retirement and make equal annual deposits into his retirement account. He intends to retire in 30 years and believes he will need to withdraw funds while retired for 20 years. He wants to withdraw $90,000 each year and believes he can invest at 8% rate. The first withdrawal will not take place until one year after he retires.

All work must be shown.

A) If he starts making these deposits in one year and makes his last deposit on the day he retires, what amount must he deposit annually to be able to make the desired withdrawals at retirement?

B) Suppose your friend just won the lottery. Rather than making annual deposits, he decides to make one lump sum deposit today to cover his retirement needs. What amount does he have to deposit today?

C) Suppose your friend’s employer will contribute $1,500 to the account each year as part of the company’s profit sharing plan. In addition, your friend expects a $25,000 distribution from a family trust 20 years from now. What amount must he deposit annually now to be able to make the desired withdrawals at retirement?

Explanation / Answer

calculation of value of retirement account at the end of 30 years (one year before withdrawal starts)
PMT = 90000
FV = 0
N = 20
I = 8

Hence PV = 883633

A. PV = 0
FV = 883633
I = 8
N = 30

Hence PMT = 7800.2

B. PMT = 0
FV = 883633
N = 30
I = 8
Hence PV = 87810

C. Present value of 25000 distribution
FV = 25000
PMT =0
I=8
N=20
PV= 5363.7

So he need to make annual payments, such that their present value = 87810 - 5363.7 = 82446

PV = 82446
FV=0
I=8
N=30
Hence PMT = 7323.5
Since his employer makes a contribution of 1500, he need to pay 7323.5 - 1500 = 5823.5

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