What would be your future account value (after-tax and after-inflation) if you invested $125 each month into a growth mutual fund for 20 years? Assume an average annual rate of return of 12.5 percent. Assume a combined federal and state income tax of 24% and an average inflation rate of 3.8% over the 20-year period.

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DeniceSandidge DeniceSandidge · Answer 1 · 2019-09-16T12:23:27+02:00

Answer:

future value is $4353.89

Explanation:

given data

invested = $125 each month

time = 20 year

rate of return = 12.5 %

federal and state income tax = 24% = 0.24

inflation rate = 3.8% = 0.038

to find out

future value (after-tax and after-inflation)

solution

first we find here real rate of return by given formula that is

1+ real rate of return = [tex]\frac{1 + nominal return rate}{1+inflation rate}[/tex] ...................1

so here nominal return rate is = 12.5% ( 1 - 24% ) = 9.5% = 0.095

so

1+ real rate of return = [tex]\frac{1 +0.095}{1+0.038}[/tex]

real rate of return = 0.05491

so real rate of return is 5.49%

so

future value formula is express as

future value = [tex]investment * \frac{(1+r)^{n} -1}{r}[/tex] ............2

put here value

future value = [tex]125 * \frac{(1+0.0549)^{20} -1}{0.0549}[/tex]

future value = 4353.89

so future value is $4353.89