Question

You are planning to save for retirement over the next 30 years. To save for retirement, you will invest $1,350 a month in a stock account in real dollars and $560 a month in a bond account in real dollars. The effective annual return of the stock account is expected to be 13 percent and the bond account will earn 6 percent. When you retire, you will combine your money into an account with an effective annual return of 8 percent. The inflation rate over this period is expected to be an effective annual rate of 3 percent.

  

a.	How much can you withdraw each month from your account in real terms assuming a withdrawal period of 25 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	What is the nominal dollar amount of your last withdrawal? (Do not round intermediate calculations and

Answer 1

1.
real return=(1+nominal return)/(1+inflation)-1

real return of stock account=1.13/1.03-1

real return of bond account=1.06/1.03-1

monthly compounded real return=((1+effective annual return)^(1/12)-1)*12

monthly compounded real return of stock account=(((1+1.13/1.03-1)^(1/12)-1)*12)
monthly compounded real return of bond account=(((1+1.06/1.03-1)^(1/12)-1)*12)

Real Future Value after 30 years=real monthly amount/(monthly compounded rate/12)*((1+monthly compounded rate/12)^(12*30)-1)

Real Total Future Value after 30 years=Stock+Bond=1350/((((1+1.13/1.03-1)^(1/12)-1)*12)/12)*((1+(((1+1.13/1.03-1)^(1/12)-1)*12)/12)^(12*30)-1)+560/((((1+1.06/1.03-1)^(1/12)-1)*12)/12)*((1+(((1+1.06/1.03-1)^(1/12)-1)*12)/12)^(12*30)-1)=2951886.503

monthly compounded real return after retirement=(((1+1.08/1.03-1)^(1/12)-1)*12)

Real Amount withdrawn each month=Future Value*(monthly compounded rate/12)/(1-1/(1+monthly compounded rate/12)^(12*25))=2951886.503*((((1+1.08/1.03-1)^(1/12)-1)*12)/12)/(1-1/(1+(((1+1.08/1.03-1)^(1/12)-1)*12)/12)^(12*25))=16828.53596

Nominal amount of last withdrawal=Real amount of first withdrawal*(1+inflation)^25=16828.53596*(1+3%)^25=35235.21718