You are planning to save for retirement over the next 24 years. To save for reti

Question

You are planning to save for retirement over the next 24 years. To save for retirement, you will invest $620 a month in a stock account in real dollars and $330 a month in a bond account in real dollars. The effective annual return of the stock account is expected to be 12 percent, and the bond account will earn 8 percent. When you retire, you will combine your money into an account with an 9 percent effective return. The inflation rate over this period is expected to be 2 percent. Assuming a 21-year withdrawal period, what will be the nominal dollar amount of the last withdraw?

Explanation / Answer

This has two investment over 24 yrs. One in stock & one in bonds.
Stocks : nper = 24 yrs=24*12 = 288, PMT = $620 pm, Return =12% SO Rate = 12%/12 monthly
SO Accumulated sum after 24 Yrs=FVs = FV(Rate,nper,PMT)
ie FVs = FV(12%/12,288,-620) = $1,026,798 .........(A)

Bonds : nper = 24 yrs=24*12 = 288, PMT = $330 pm, Return =8%. SO Rate = 8%/12 monthly
SO Accumulated sum after 24 Yrs=FVb = FV(Rate,nper,PMT)
ie FVb= FV(8%/12,288,-330) = $285,993 .........(B)
So at end of 24 Yrs, Total Sum is A+B = $1,312,791

Now this is invested for nper= 21 Yrs=21*12= 252 period.
PV = $1,312,791. FV=0.
Return is 9%. Inflation is 2%. So effective return is 9%-2% = 7%
SO Rate = 7%/12 assuming monthly withdrawls
SO Monthly withdrawl PMT = PMT(Rate,nper,PV,FV)
ie PMT = PMT(7%/12, 252,-1312791,0) = $9,957
SO he can withdraw $9,957 pm for 21 Yrs.
Last wothdrawl is $9,957

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