Question

Make sure the formatting is nice and easy to understand. No "HAND WRITTEN" answer.

You are 30 and have decided you need to start saving for retirement in your 401(k) by depositing $1,325 per month. You are splitting your money between two investment options: 60% in Fund Aggressive which is expected to earn 10.5% annually and 40% in Fund Conservative which is expected to earn 5% annually. Once you retire at 65 and want to be sure that your spending lasts for 30 years. How much can you spend per month in retirement? Assume a 6% discount rate in retirement.

Answer 1

Monthly savings in Aggressive Fund=1325*60%=795

Monthly savings in Conservative Fund=1325*40%=530

Future Value=Future Value of ordinary annuity=Monthly savings/(rate/12)*((1+rate/12)^(12*n)-1)

Savings period n=12*(65-30)=12*35

Future Value of Aggressive Fund=795/(10.5%/12)*((1+10.5%/12)^(12*35)-1)=3436497.469

Future Value of Conservative Fund=530/(5%/12)*((1+5%/12)^(12*35)-1)=602128.9854

Total Future Value=3436497.469+602128.9854=4038626.454

Monthly spendings=Monthly annuity=Present Value of annuity*(rate/12)/(1-1/(1+rate/12)^(12*n))

Retirement period n=12*30

Monthly spendings in retirement=4038626.454*(6%/12)/(1-1/(1+6%/12)^(12*30))=24213.60611