Question

Jim and Sue are planning to retire on January 1, 1995. Their goal is to have enough money in savings to be able to withdraw $3,000 per month beginning one month after retirement and continuing for 25 years after retirement. They earn an annual effective rate of interest of 10% on their account.

Determine the minimum amount needed in their savings account on January 1, 1995, to accomplish their goal.

A.    Less than $325,000

B.    At least $325,000, but less than $335,000

C.    At least $335,000, but less than $345,000

D.    At least $345,000, but less than $355,000

E.    At least $355,000

Answer 1

- Periodic Withdrwals per month beginning one month after retirement = $ 3000

Annual Effective rate(EIR) = 10%

Calculating the Nominal rate of return:-

Let r be the Nominal interest rate

m = no of times compounding in a year = 12

1.10 = (1+r/12)^12

Taking 12root of both sides

1.00797414 = (1+r/12)

r/12 = 0.00797414

r = 9.569%

Calculating the Present value of periodic withdrawals on retirement date as withdrawals started one month after retirement:-

Where, C= Periodic withdrawals = $ 3000

r = Periodic Interest rate = 0.09569/12 = 0.007974166

n= no of periods = 25 years*12 = 300

Present Value = $ 341,492.01

So, the the minimum amount needed in their savings account on January 1, 1995 is $ 341,492.01

hence, option C

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