$6000 is deposited into an account. It grows to $10000 in 8 years. What is the interest rate assuming an annual compound?
I'm not exactly sure what to do please help!
Hello, civiliam!
You're expected to know the compound interest formula: . $\displaystyle A \;=\;P(1 + i)^n$$6000 is deposited into an account. It grows to $10000 in 8 years.
What is the interest rate assuming an annual compound?
. . where: .$\displaystyle \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: .$\displaystyle P = 6,\!000,\;\;n =8,\;\;A =10,\!000 $
The equation becomes: .$\displaystyle 10,\!000 \;=\;6,\!000(1+i)^8 \quad\Rightarrow\quad (1+i)^8 \:=\:\frac{10,\!000}{6,\!000} \:=\:\frac{5}{3}$
Take the 8th root of both sides: .$\displaystyle 1 + i \:=\:\left(\frac{5}{3}\right)^{\frac{1}{8}} \quad\Rightarrow\quad i \:=\:\left(\frac{5}{3}\right)^{\frac{1}{8}} - 1$
Therefore: .$\displaystyle i \;=\;0.065935911 \;\approx\;6.6\% $