### Home > CCA2 > Chapter 8 > Lesson 8.3.2 > Problem8-157

8-157.

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 $25{,}000$?

This is an exponential function of the form $y = ab^x$, where a is the initial value, $b$ is the multiplier, $x$ is the number of years, and $y$ is the amount of money saved.

Substitute the values given into the equation.

Divide both sides by $15000$.

Remember the Power Property of Logarithms and take the log of both sides.

Solve for $t.$

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

$25000 = 15000(1.08)^t$

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

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

$t=6.64$