Question

Marvin the Martian is thinking about retirement. He wants to be able to withdraw $5,450 from his retirement account every quarter for the next 15 years. If his bank pays a nominal annual rate of 6.25% compounded weekly, how much money does Marvin the Martian need to deposit in his retirement account today to be able to complete each quarterly withdrawal for the next 15 years?

Answer 1

Marvin wants to withdraw an amount of 5450 in every quarter for 15 years. It is an annuity problem where the withdrawal amount is the regular cash flow and we have to find the PV of the annuity i.e. the deposit that has to be made.

Time period (n) = 15*4 = 60 quarters

Withdrawal amount (A) = 5450

Interest rate = 6.25% annaully = 6.25%/52 weekly = 0.120%

In one quarter there are 12 weeks so,

Interest rate for a qaurter (i) = (1.0012)^12 - 1 = 1.45%

Formula for PV of annuity is:

PV = A*{1 - (1+i)^(-n)}/i

=> PV = 5450*{1 - 1.0145^(-60)}/0.0145

=> PV = 217407.262

Marvin the Martian need to deposit in his retirement account today = 217407.262