Question

You are planning to save for retirement over the next 30 years. To save for retirement, you will invest $1,150 per month in a stock account in real dollars and $540 per 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 return of 8 percent. The returns are stated in nominal terms. The inflation rate over this period is expected to be 3 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.)

Monthly withdrawal

$

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.)

Last withdrawal

$

Answer 1

First we calculate amount we will have after 30 years in stock and bond account. we can use financial calculator with below key strokes to find out future values in these 2 accounts.

Stock account

N= no. of months = 30*12 = 360; PMT= monthly deposit = $1,150; PV = present value = 0; I/Y= return = 13.00%/12 = 1.083% > CPT = compute > FV = future value = $5,024,713

So, Stock account will have $5,024,713 after 30 years.

Bond Account

N= no. of months = 30*12 = 360; PMT= monthly deposit = $540; PV = present value = 0; I/Y= return = 6.00%/12 = 0.5% > CPT = compute > FV = future value = $542,438

So, Bond account will have $542,438 after 30 years.

Now $5,024,713+$542,438 = $5,567,151 put into a retirement account earning 8%. We need to calculate monthly withdrawal amount in real dollars.

so we need to use real rate of return for calculation of monthly withdrawal amount in real dollars.

(1+nominal return) = (1+real return)*(1+inflation rate)

real rate of return = [(1+nominal rate of return)/(1+inflation rate)] - 1 = [(1+0.08)/(1+0.03)] - 1 = (1.08/1.03) - 1 = 1.048543689320388 - 1 = 0.0485 or 4.85%

Monthly withdrawal:

N= no. of months = 25*12 = 300; FV = future value = $0; PV = present value = $5,567,151; I/Y= return = 4.85%/12 = 0.40416% > CPT = compute > PMT = monthly withdrawal = $32,060.08

So, monthly withdrawal amount in real dollars is $32,060.08.

For calculation of nominal dollar amount of last withdrawal, we will multiply real monthly withdrawal amount with 1+inflation rate. we will withdraw equal amount every month. so all the withdrawals are same.

Last withdrawal = $32,060.08*(1+0.03) = $32,060.08*1.03 = $33,021.88

So, nominal dollar amount of your last withdrawal is $33,021.88.