### Home > INT3 > Chapter 9 > Lesson 9.2.2 > Problem9-113

9-113.

A long-lost relative died and has 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 $25,000$? Homework Help ✎

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.

$25000 = 15000\left(1.08\right)^{t}$

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

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

$t = 6.64$