Use the appropriate compound interest formula to compute the balance in the account after the stated period of time

​$13 comma 00013,000 

is invested for 

99 

years with an APR of 

44​% 

and quarterly compounding.

Question content area bottom

Part 1

The balance in the account after 

9

years is 

​$enter your response here.

​(Round to the nearest cent as​ needed.)

To compute the balance in an account using compound interest, we use the following formula:

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

Where:
- $ A $ is the amount of money accumulated after $ t $ years, including interest.
- $ P $ is the principal amount (initial investment).
- $ r $ is the annual interest rate (in decimal form).
- $ n $ is the number of times the interest is compounded per year.
- $ t $ is the time the money is invested for, in years.

### Given:
- $ P = 13,000 $ (the principal amount)
- $ r = 4\% = 0.04 $ (annual percentage rate)
- $ n = 4 $ (since interest is compounded quarterly)
- $ t = 9 $ years

Now, substituting the values into the formula:

\[
A = 13,000 \left(1 + \frac{0.04}{4}\right)^{4 \times 9}
\]

Let me calculate this for you.The balance in the account after 9 years, with an APR of 4% and quarterly compounding, is approximately **$18,600** (rounded to the nearest cent).

Would you like further clarification on any steps?

Here are 5 related questions to deepen your understanding:
1. What would the balance be if the compounding were done monthly instead of quarterly?
2. How does changing the APR affect the final balance after 9 years?
3. How would the balance change if the time period was 15 years instead of 9?
4. What is the difference between simple and compound interest, and how does it impact long-term investments?
5. How do different compounding intervals (annually, semi-annually, etc.) affect the final amount?

**Tip**: The more frequently interest is compounded, the higher the accumulated amount will be over time due to "interest on interest."

Use the appropriate compound interest formula to compute the balance in the account after the stated period of time. $13,000 is invested for 9 years with an APR of 4% and quarterly compounding. The balance in the account after 9 years is $enter your response here. (Round to the nearest cent as needed.)

Learn how to calculate compound interest on a $13,000 investment over 9 years with an APR of 4% and quarterly compounding. This example demonstrates the use of the compound interest formula, showing how to find the final balance in the account, rounded to the nearest cent. Suitable for Grades 10-12.

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