CPM Homework Help : A2C Problem 9-157

A long lost relative died and left you $$15,000$ ! Your parents say that you need to save the money for college, so you put it an account that pays 8% interest compounded annually. How many years will it take until your account is worth $$25,000$ ?

Step 1:

Remember the annual compound interest formula.
$A = P\left(1 + r\right)^{t}$

Step 2:

First substitute the values into the equation.
25000 = 15000(1.08)^t

Step 3:

Divide both sides by 15000.

$\frac{5}{3}=(1.08)^{\textit{t}}$

Step 4:

Remember the rules of logarithms and take the log of both sides.

$\text{log}\left(\frac{5}{3}\right)=\textit{t}(\text{log}1.08)$

Step 5:

Solve for t.

Answer:

The account will be worth 25000 in between 6 and 7 years.

$t = 6.64$