Question

Bob wants to retire in 15 years when he turns 62. Bob wants to have enough money to replace 75% of his current income less what he expects to receive from Social Security at the beginning of each year. He expects to receive $25,714 per year from Social Security in today’s dollars at full retirement age of 67. However, he will take Social Security early at age 62, when he retires. Bob is aggressive and wants to assume an 8% annual investment rate of return and that inflation will be 3% per year. Based on his family history, Bob expects that he will live 30 years in retirement (age 92). If Bob currently earns $80,000 per year and he expects his raises to equal the inflation rate, how much does he need at retirement to fulfill his retirement goals?

Answer 1

$1,072,458

Explanation:

Bob currently earns $80,000

Income replacement ratio (the percentage of pre-retirement income needed in retirement)= 75% less current Social Security Social Security at FRA = $25,741. The social Security at age 62 needs to be reduced by 30%, which equals $18,000. $42,000 = [($80,000 x 75%)-$18,000]

so we have:

N=15

I=3%

PV=$42,000

PMT=0

FV=$65,434.63

N=30

I=4.85436% [(1.08 / 1.03) - 1] x 100 PMT=$65,434.63

PV=$1,072,457.81

FV=0