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The problem in the image involves calculating how long it will take for an investment of $15,000 to grow to $60,000, given a 12% APR compounded monthly.

The formula used for compound interest is:

\[
S = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $S$ is the future value of the investment ($60,000).
- $P$ is the initial investment ($15,000).
- $r$ is the annual interest rate (12% or 0.12).
- $n$ is the number of times interest is compounded per year (12 for monthly compounding).
- $t$ is the number of years, which we need to solve for.

We can rearrange the formula to solve for $t$:

\[
t = \frac{\ln\left(\frac{S}{P}\right)}{n \ln\left(1 + \frac{r}{n}\right)}
\]

Now, let's calculate the value of $t$. I'll perform this calculation.

At the end of t years, the future value of an investment of $15,000 in an account that pays 12% APR compounded monthly is $60,000. How long will it take for the investment to amount to $60,000?

Learn how to calculate the time required for an investment of $15,000 to grow to $60,000 in an account with 12% APR compounded monthly. This solution explains the use of the compound interest formula and provides a detailed step-by-step process.

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