You are planning to save for retirement over the next 25 years. To do this, you will invest $730 per month in a stock account and $330 per month in a bond account. The return of the stock account is expected to be 9.3 percent, and the bond account will pay 5.3 percent. When you retire, you will combine your money into an account with a return of 6.3 percent. How much can you withdraw each month from your account assuming a 20-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 · 2020-10-07T03:09:48+02:00

Answer:

The monthly withdrawal will be of $ 7.823,24

Explanation:

We solve for the future value of each investment:

stock account:

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

C 730

time 300 (25 years x 12 month per year)

rate 0,00775 (9.3% among 12 months)

[tex]730 \times \frac{(1+0,00775)^{300} -1}{0,00775} = FV\\[/tex]

FV $860.498,28

bond account:

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

C 330

time 300

rate (5.3% annual among 12 months) 0,004416667

[tex]330 \times \frac{(1+0,00441667)^{300} -1}{0,00441667} = FV\\[/tex]

FV $205.563,2522

now, we add them:

860498.28 + 205.563,25 = $1.066.061,53

And last, solve for the monthly withdrawal of this sum:

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

PV $1.066.061,53

time 240 (20 years x 12 months)

rate 0,00525 (6.3% among 12 months)

[tex]1066061,53 \div \frac{1-(1+0,00525)^{-240} }{0,00525} = C\\[/tex]

C $ 7.823,244