Question

You are planning to save for retirement over the next 30 years. To save for retirement, you will invest $800 per month in a stock account in real dollars and $400 per month in a bond account in real dollars. The effective annual return of the stock account is expected to be 11 percent, and the bond account will earn 7 percent. When you retire, you will combine your money into an account with an effective return of 9 percent. The returns are stated in nominal terms. The inflation rate over this period is expected to be 4 percent.

How much can you withdraw each month from your account in real terms assuming a 25-year withdrawal period? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

What is the nominal dollar amount of your last withdrawal? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Real rate=((1+Nominal Rate of return)/(1+Inflation rate))-1

Real rate (stock a/c)=((1+11%)/(1+4%))-1=

6.73%

Monthly real rate=6.73%/12=0.56% or 0.0056

Real rate (Bond a/c)=((1+7%)/(1+4%))-1=

2.88%

Monthly real rate=2.88%/12=0.24% or 0.0024

Reat rate of the Combined a/c=((1+9%)/(1+4%))-1

4.81%

Monthly real rate=4.81%/12=0.40% or 0.0040

Using the above real interest rates,

Future value of the month-end annuities at end of 30 yrs., ie 30*12=360 months

at respective real rates will be as follows:

Using the FV of Ordinary annuity formula,

FV(OA)=Mthly Pmt.*((1+Mthly r)^360-1)/Mthly r=

On stocks:

FV(OA)=800*(1.0056^360-1)/0.0056=

923732.2099

On bonds

FV(OA)=400*(1.0024^360-1)/0.0024=

228362.9202

so, the Present value of the combined money at end of 30 yrs will be

923732+228363=

1152095

(in real terms)

1..Amt. of withdrawal each month from this combined a/c in real terms assuming a 25-year withdrawal period can be found out by using

the formula for PV of ordinary annuity ,

PV(OA)=Mthly pmt.*(1-(1+ mthly r)^-n)/Mthly r

where n= 25 yrs. *12 mths.= 300

PV= $ 1152095,

& real interest rate for the combined a/c = 0.0040 (as calculated above)

so,

1152095=Mthly .amt.*(1-1.0040^-300)/0.0040

Solving the above, the monthly withdrawal , at real $ terms, during the 25 yr-withdrawal period will be:

6601.47   (ANSWER)

2.Nominal amt. of last withdrawal is

Taking into account the compounding effect of inflation, ie. 4%/12=0.0033 p.m., for (30+25)=55 yrs.

6601.47*(1.0033)^(55*12)=

58073.33

(ANSWER)