Investment Problem find rate

Hello, civiliam!

Quote:

$6000 is deposited into an account. It grows to $10000 in 8 years.
What is the interest rate assuming an annual compound?

You're expected to know the compound interest formula: . $A \;=\;P(1 + i)^n$

. . where: . $\begin{Bmatrix}P &=& \text{principal deposited} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \\ A &=& \text{Final balance} \end{Bmatrix}$

We are given: . $P = 6,\!000,\;\;n =8,\;\;A =10,\!000$

The equation becomes: . $10,\!000 \;=\;6,\!000(1+i)^8 \quad\Rightarrow\quad (1+i)^8 \:=\:\frac{10,\!000}{6,\!000} \:=\:\frac{5}{3}$

Take the 8th root of both sides: . $1 + i \:=\:\left(\frac{5}{3}\right)^{\frac{1}{8}} \quad\Rightarrow\quad i \:=\:\left(\frac{5}{3}\right)^{\frac{1}{8}} - 1$

Therefore: . $i \;=\;0.065935911 \;\approx\;6.6\%$