Question

You are planning to save for retirement over the next 30 years. To do this, you will invest $750 per month in a stock account and $250 per month in a bond account. The return of the stock account is expected to be 10 percent, and the bond account will pay 6 percent. When you retire, you will combine your money into an account with a return of 5 percent. How much can you withdraw each month from your account assuming a 25-year withdrawal period? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

The withdrawals will be of $ 11,379.014 per month

Step-by-step explanation:

Future value of the annuities:

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 750.00

time 360(30 years x 12 monhs per year)

rate 0.008333333 (10% / 12 months)

`750 * (1-(1+0.00833)^(-360) )/(0.008333) = PV\\`

PV $1,695,365.9436

`C * ((1+r)^(time) -1)/(rate) = PV\\`

C 250.00

time 360 (30 years x 12 monhs per year)

rate 0.005 (6% / 12 months)

`250 * ((1+0.005)^(360) -1)/(0.005) = PV\\`

PV $251,128.7606

Total 1,695,365.84 + 251,128.76 = 1.946.494,6‬

and from here we withdraw for 25 years:

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV 1,946,495

time 300 (25 years x 12 months)

rate 0.004166667 (5% / 12 months)

`1946494.6 / (1-(1+0.004167)^(-300) )/(0.004167) = C\\`

C $ 11,379.014