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

​$8 comma 0008,000 

is invested for 

1919 

years with an APR of 

22​% 

and monthly compounding.

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Part 1

The balance in the account after 

1919 

years is 

​$enter your response here.

To calculate the balance in the account after 19 years with monthly compounding, you can use the compound interest 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 (the initial amount of money), which is $8,000.
- $ r $ is the annual interest rate (as a decimal), which is 2% or 0.02.
- $ n $ is the number of times that interest is compounded per year, which is 12 for monthly compounding.
- $ t $ is the time the money is invested for, in years, which is 19 years.

Let's plug in the values:

\[
A = 8000 \left(1 + \frac{0.02}{12}\right)^{12 \times 19}
\]

Now, let's calculate it.

\[
A = 8000 \left(1 + \frac{0.02}{12}\right)^{228}
\]
\[
A = 8000 \left(1 + 0.0016667\right)^{228}
\]
\[
A = 8000 \left(1.0016667\right)^{228}
\]

Let's compute this value.The balance in the account after 19 years with monthly compounding is approximately **$11,694.58**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the balance change if the interest were compounded quarterly instead of monthly?
2. What happens to the final amount if the APR is increased to 5%?
3. How does the number of compounding periods per year affect the final amount?
4. Can you calculate the interest earned alone in this scenario?
5. How would the formula change if the interest were compounded continuously?

**Tip:** Monthly compounding increases the final amount compared to annual compounding because interest is added more frequently.

Learn how to calculate compound interest with monthly compounding. Solve for the balance after 19 years with $8,000 invested at an APR of 2%. Includes step-by-step solution using the compound interest formula. Suitable for advanced high school students.

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