Question

# You are planning to save for retirement over the next 25 years. To do this, you...

You are planning to save for retirement over the next 25 years. To do this, you will invest \$3,000 a quarter in a stock account and \$1,000 a quarter in a bond account. These investments will be made at the beginning of each quarter. The return of the stock account is expected to be 8%, and the bond account will pay 4%. When you retire, you will combine your money into an account with a 6% return. How much can you withdraw each month (starting one month from the retirement date) from your account assuming a 20-year withdrawal period?

Assuming rate compounded quarterly before retirement and rate compounded monthly after retirement for simplicity

Step 1:
As the savings are beginning of period it is an annuity due
Future value of annuity due=AMount/(periodic rate)*((1+periodic rate)^n-1)*(1+periodic rate)

Step a) Find the future value of stock account
=3000/(8%/4)*((1+8%/4)^(4*25)-1)*(1+8%/4)
=955430.8561

Step b) Find the future value of bond account
=1000/(4%/4)*((1+4%/4)^(4*25)-1)*(1+4%/4)
=172186.1968

Step c) Find total future value
=955430.8561+172186.1968
=1127617.053

Step 2: Find monthly withdrawals
As the withdrawals are end of the period it is an ordinary annuity
Periodic payments in ordinary annuity=Value*periodic rate/(1-1/(1+periodic rate)^n)
=1127617.053*(6%/12)/(1-1/(1+6%/12)^(12*20))
=8078.598788