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The problem asks to determine the number of years required for an investment of $15,000 to grow to $91,221.04, given a 5% annual interest rate with interest compounded yearly.

We can solve this using the formula for compound interest:

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

Where:
- $ A $ is the final amount ($91,221.04),
- $ P $ is the initial principal ($15,000),
- $ r $ is the annual interest rate (5% or 0.05),
- $ n $ is the number of times the interest is compounded per year (1, since it's compounded yearly),
- $ t $ is the time in years (which we need to find).

Rearranging the formula to solve for $ t $:

\[
t = \frac{\ln(A/P)}{n \cdot \ln(1 + r/n)}
\]

Substituting the values:

\[
t = \frac{\ln(91,221.04 / 15,000)}{1 \cdot \ln(1 + 0.05/1)}
\]

Now, let me calculate this for you.The time required for the investment to grow to $91,221.04 at an interest rate of 5% compounded yearly is approximately 37 years.

Would you like more details on any part of this solution? Here are some related questions you might find useful:

1. What happens if the interest rate is compounded monthly instead of yearly?
2. How does increasing the interest rate affect the time to reach a specific amount?
3. Can you explain how compound interest differs from simple interest?
4. What would the final amount be after 30 years at the same interest rate?
5. How does the initial investment affect the time required to reach a target amount?

**Tip:** Always double-check whether interest is compounded annually, monthly, or daily, as this significantly impacts the growth of the investment!

15,000$ is invested in an account that yields 5% interest per year. After how many years will the account be worth 91,221.04$ if the interest is compounded yearly?

Discover how long it takes for an investment of $15,000 to grow to $91,221.04 with a 5% annual interest rate, compounded yearly. This problem explores key concepts of compound interest, exponential growth, and logarithms. Suitable for students in Grades 10-12.

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