Joe, age 25, saves 5% of his $67,000 salary at the end of each year for the next

Question

Joe, age 25, saves 5% of his $67,000 salary at the end of each year for the next 30 years as a part ofhis retirement plan that pays 8% annual interest. Once the 30 deposits are made, Joe lets his account accumulate interest but waits to 4)withdraw until he retires. Joe retires when he is 65 and decidesto withdraw equal amounts for the next 20 years at which time he'll have no money left. How much money can Joe withdraw each year at the beginning of the year starting when he retires for 20 years of equal payments? Annual Withdrawals 4)

Explanation / Answer

5% of Salary = 5%* 67000 = 3350
Time = 30 years
FV after 30 years at age 55 = 3350 * ((1+r)n-1)/r = 3350 * ((1+5%)30-1)/5% = 222570.14
FV of this aamount at age 65 = 222570.14*1.05^10 = 362,543.30

20 equal withdrawals annuity due of
362,543.20 = (1+r) * annuity due* ( 1-(1+r)-n)/r
362,543.20 = (1+5%) * annuity due* ( 1-(1+5%)-20)/5%
Annuity due or annual withdrawals = 29,091.44

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