CPM Homework Help : CCA2 Problem 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$ ?

Step 1:

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.

Step 2:

Substitute the values given into the equation.

Step 3:

Divide both sides by $15000$ .

Step 4:

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

Step 5:

Solve for $t.$

Answer:

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

$25000 = 15000(1.08)^t$

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

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

$t=6.64$