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The question states:

Relative to your current age, the present value at age 67 found in question #1 becomes the future value you need to obtain given your current age now, How much money do you need to deposit starting today in order to obtain the present value calculated above at age 67? Suppose your currently 25 years old and assume a 4% growth rate.

The $PV$ value I obtained earlier is $\$66,647.58$.

This is my attempt:

Using the future value of an annuity formula $FV = C \cdot \dfrac{(1+r)^n - 1}{r}$:

$⇒ C = \dfrac{FV}{\frac{(1+r)^n - 1}{r}}$

$= \dfrac{66,647.58}{\frac{(1+0.04)^{12⋅(67-25)} - 1}{0.04}}$

$= 0.000006935$

I know this is wrong, so did I use the incorrect future value formula?

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1 Answer 1

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Hint: You have to use the (relative) monthly interest rate $i_{12}=\frac{0.04}{12}$, due the monthly compounding.

$$ C=\dfrac{66647.58}{\frac{(1+\frac{0.04}{12})^{12⋅42} - 1}{\frac{0.04}{12}}} $$

See here the result.

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