Question

# Problem #3 Rup is planning to retire in 35 years. He wishes to deposit a regular...

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?

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

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