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A man aged 40 wishes to accumulate a fund for retirement by depositing $1,000 at the beginning of each year for 25 years. Strating at age 65, he will make 15 annual withdrawls at the beginning of each year. Assuming that all payments are certain to be made, find the amount of each withdrawal starting at age 65 if the annual percentage rate (compunded annually) is 4% during the first 25 years but only 3.5% thereafter.

Respuesta :

TomShelby

Answer:

The man will made 15 drawins for 31,468 at their retirement age.

Explanation:

We solve for the future value of the annuity-due (deposits at the beginning)

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

C 1,000.00

time      25

rate         0.04

[tex]1000 \times \frac{(1+0.04)^{-25} -1}{0.04}(1+0.04) = PV\\[/tex]

FV $375.1168

Now, we calcualte the amount of the withdrawals considering the new rate:

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

[tex]375.116802253964 \div \frac{1-(1+0.035)^{-15} }{0.035}(1+0.035) = C\\[/tex]

C  $ 31.468

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