Use the appropriate compound interest formula to compute the balance in the account after the stated period of time
​$5 comma 0005,000 is invested for 1919 years with an APR of 3.013.01​% and monthly compounding.
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Part 1
The balance in the account after 1919 years is ​$enter your response here.
​(Round to the nearest cent as​ needed.)

To compute the balance in the account after 19 years with an APR of 3.01% and monthly compounding, we 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 (decimal form).
- $n$ is the number of times the interest is compounded per year.
- $t$ is the number of years.

Given:
- $P = 5000$
- $r = 3.01\%$ or $0.0301$ in decimal form.
- $n = 12$ (since the interest is compounded monthly).
- $t = 19$ years.

Now we can plug these values into the formula and calculate the balance.

\[
A = 5000 \left(1 + \frac{0.0301}{12}\right)^{12 \times 19}
\]

Let's calculate this.The balance in the account after 19 years is **$8,851.81**.

Would you like more details or have any other questions?

Here are some related questions:
1. What if the interest was compounded quarterly instead of monthly?
2. How would the final amount change if the APR were increased to 4%?
3. What happens if the investment duration is shortened to 10 years?
4. How does the compound interest formula differ from simple interest?
5. Can you compute the interest earned separately from the total balance?

**Tip:** The more frequent the compounding period (monthly, daily), the higher the final balance due to interest-on-interest effects.

Use the appropriate compound interest formula to compute the balance in the account after the stated period of time. $5,000 is invested for 19 years with an APR of 3.01% and monthly compounding. The balance in the account after 19 years is ​$ (Round to the nearest cent as needed).

Learn how to calculate compound interest for an investment of $5,000 over 19 years with an APR of 3.01% and monthly compounding. This solution includes a step-by-step explanation using the compound interest formula and is suitable for high school students in Grades 10-12.

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