# Math Help - Simple Problem!!

1. ## 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?

2. 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: . $r \;=\;0.16652904 \;\approx\;16.65\%$