You plan to retire 24 years from now, and you expect that you will live 35 years

Question

You plan to retire 24 years from now, and you expect that you will live 35 years after retiring. You want to have enough money upon reaching retirement age to withdraw $175,000 from the account at the beginning of each year you expect to live, and yet still have $1,000,000 left in the account at the time of your expected death. You plan to accumulate the retirement fund by making equal bi-weekly deposits at the end of each two week period for the next 24 years. You expect that you will be able to earn a quoted rate of 10%, compounded semi-annually on your deposits. However, you only expect to earn an EAR of 5% on your investment after you retire since you will choose to place the money in less risky investments. What equal bi-weekly deposits must you make to reach your retirement goal?

Explanation / Answer

Details EAR after Retirement =5% PV of Retirement Annuity due =(A*[(1+k)^n-1]/k(1+k)^n)*(1+k) Given A =175,000 n=35 years k=5% pa PV =175000*(1.05^35-1)/(0.05*1.05^35) PV =3,500,000 So the PV of Annuity fund after 24 Years=                   3,500,000 PV of 1,000,000 left after 35 years =$1M/1.05^35=                       181,290 Total PV of the fund required after 24 Years =                   3,681,290 Ineterst rate before retirement =10% compounded semi annually EAR =(1+0.10/2)^2-1= 10.25% So EAR =10.25% pa Biweekly Effective interest rate =10.25%/26= 0.3942% Annuity FV formula = =(A*[(1+k)^n-1]/k k=0.3942% n=24*26=624 bi weeks A = Bii weekly deposit rate   3681290= A*[1.003942^624-1)/0.003942 A =1363.09 Sao Bi weekly deposit required =$1,363.09

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