Question

Problem #3

Rup is planning to retire in 35 years. He wishes to deposit a regular amount every quarter until he retires so that, beginning one-year following his retirement, he will receive annual payment of $100,000 for the next 20 years. The interest rate is 10% compounded monthly.

1. How much money he must have in his savings account at retirement?

2. How much money must he deposit every quarter for the next 35 years?

Answer 1

a)

Annual withdrawal =W=$100,000

Effective rate of interest per year=(1+10%/12)^12-1=0.104713

Number of withdrawals=n=20

Money at the time of retirement=W*(P/A,0.104713,20)=100000*(P/A,0.104713,20)

Let us calculate the interest factors in this case

Money at the time of retirement=R=100000*8.24671552=$824,671.55

b)

Effective quarterly interest rate=(1+10%)^3=0.025209

Number of quarters till retirement=n=35*4=140

Quarterly deposit=R*(A/P,0.025209,140)=824671.55*(A/P,0.025209,140)

Let us calculate the interest factor

Quarterly deposit=824671.55*0.00079677=$657.07