it is estimated that you will pay about $80,000 into the social security system
ID: 1247579 • Letter: I
Question
it is estimated that you will pay about $80,000 into the social security system (FICA) over your 40 year work span. for simplicity, assume this is an annuity of $2,000 per year, starting with your 26th birthday and continuing thought your 65th bithday.a. what is the future equivalent worth of your social security savings when you retire at age 65 if the goverment's interest rate is 6% per year?
b. what annual withdrawal can you make if you expect to live 20 years in retirement? let i= 6% per year.
Explanation / Answer
We have PMT = $2000, N= 40 Yrs, I = 6% 1. We have to find FV of Annuity = FVA40 = PMT*FVIFA40,6% ie FVA40 = PMT*[(1+I)^N -1]/I = 2000*[(1+6%)^40 -1]/6% = 2000*154.76 = $309,520 So Future value of Social secuity contn of $2000 for 40 yrs is $309,520 2. Here PV = 309520, I=6%, N=20 Yrs, FV=0. We have to find PMT Using Excel PMT function, we get Annual withdrawl = PMT(Rate, nper,PV) ie Annual withdrawl = PMT(6%,20,-309520) = $26,985.36
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