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Math Help - Simple Problem!!

  1. #1
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    Simple Problem!!

    I'm sure this is simple and uses the present value formula somehow, but I don't know the exact formula!!

    For an investment to grow fourfold in 9 years, at what annual rate must the investment grow?
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  2. #2
    Super Member

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    Hello, DooBeeDoo!

    You just need the Compound Interest Formula . . .


    For an investment to grow fourfold in 9 years,
    at what annual rate must the investment grow?

    Assuming that investment is compounded annually,
    . . the formula is: . A \;=\;P(1 + r)^n

    . . where: . \begin{Bmatrix}A & = & \text{final amount} \\ P & = & \text{principal invested} \\ r & = & \text{annual interest rate} \\ n & = & \text{number of years} \end{Bmatrix}


    In this problem, we have: . P\text{ dollars invested},\;A \:=\:4P,\;n = 9

    We have: . P(1 + r)^9 \:=\:4P\quad\Rightarrow\quad(1 + r)^9 \:=\:4

    Take the 9th root: .  1 + r \:=\:4^{\frac{1}{9}}\quad\Rightarrow\quad r \:=\:4^{\frac{1}{9}} - 1


    . . Therefore: . r \;=\;0.16652904 \;\approx\;16.65\%

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