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.)

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TomShelby TomShelby · Answer 1 · 2020-02-05T07:36:40+01:00

Answer:

The withdrawals will be of $ 11,379.014 per month

Explanation:

Future value of the annuities:

[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

C 750.00

time 360(30 years x 12 monhs per year)

rate 0.008333333 (10% / 12 months)

[tex]750 \times \frac{1-(1+0.00833)^{-360} }{0.008333} = PV\\[/tex]

PV $1,695,365.9436

[tex]C \times \frac{(1+r)^{time} -1}{rate} = PV\\[/tex]

C 250.00

time 360 (30 years x 12 monhs per year)

rate 0.005 (6% / 12 months)

[tex]250 \times \frac{(1+0.005)^{360} -1}{0.005} = PV\\[/tex]

PV $251,128.7606

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

and from here we withdraw for 25 years:

[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]

PV 1,946,495

time 300 (25 years x 12 months)

rate 0.004166667 (5% / 12 months)

[tex]1946494.6 \div \frac{1-(1+0.004167)^{-300} }{0.004167} = C\\[/tex]

C $ 11,379.014