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