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?
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: .$\displaystyle A \;=\;P(1 + r)^n$
. . where: .$\displaystyle \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: .$\displaystyle P\text{ dollars invested},\;A \:=\:4P,\;n = 9$
We have: .$\displaystyle P(1 + r)^9 \:=\:4P\quad\Rightarrow\quad(1 + r)^9 \:=\:4$
Take the 9th root: .$\displaystyle 1 + r \:=\:4^{\frac{1}{9}}\quad\Rightarrow\quad r \:=\:4^{\frac{1}{9}} - 1 $
. . Therefore: .$\displaystyle r \;=\;0.16652904 \;\approx\;16.65\%$