Suppose that ​$60 comma 000 is invested at 5​% interest. Find the amount of money in the account after 8 years if the interest is compounded annually.

To solve the problem of finding the amount of money in an account after 8 years with compound interest, we can use the compound interest formula:

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

Where:
- $ A $ is the amount of money in the account after interest,
- $ P $ is the principal amount (initial investment),
- $ r $ is the annual interest rate (as a decimal),
- $ n $ is the number of times the interest is compounded per year,
- $ t $ is the number of years.

### Given:
- $ P = 60,000 $,
- $ r = 5\% = 0.05 $,
- $ n = 1 $ (compounded annually),
- $ t = 8 $ years.

Substitute the values into the formula:

\[
A = 60,000 \left(1 + \frac{0.05}{1}\right)^{1 \times 8}
\]

Simplifying the equation:

\[
A = 60,000 \left(1.05\right)^8
\]

Now calculate:

\[
A = 60,000 \times (1.477455)
\]

\[
A \approx 88,647.30
\]

Thus, the amount of money in the account after 8 years is approximately **$88,647.30**.

Would you like more details or have any questions about this calculation?

Here are some related questions you might explore:
1. What if the interest was compounded quarterly instead of annually?
2. How would the final amount change if the interest rate was 6% instead of 5%?
3. What would be the amount after 10 years instead of 8?
4. How much interest was earned over the 8 years?
5. What is the formula for continuous compound interest?

**Tip:** The more frequently interest is compounded, the higher the final amount will be.

Suppose that $60,000 is invested at 5% interest. Find the amount of money in the account after 8 years if the interest is compounded annually.

Discover how to calculate compound interest for a $60,000 investment at 5% annual interest over 8 years. Using the compound interest formula, find the final amount in the account, approximately $88,647.30. Perfect for students in Grades 9-12 studying exponential growth and finance.

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