Use the appropriate compound interest formula to compute the balance in the account after the stated period of time
​$2 comma 000 is invested for 13 years with an APR of 3.35​% and monthly compounding.
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Part 1
The balance in the account after 13 years is ​$

enter your response here.
​(Round to the nearest cent as​ needed.)

To compute the balance in the account after a given period of time with compound interest, we use the compound interest formula:

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

Where:
- $ A $ is the final amount (the balance after the time period).
- $ P $ is the initial principal (the amount invested), which is \$2,000.
- $ r $ is the annual interest rate (APR), which is 3.35% or 0.0335.
- $ n $ is the number of times the interest is compounded per year (since it’s compounded monthly, $ n = 12 $).
- $ t $ is the time the money is invested or borrowed for, in years (which is 13 years).

Now let's substitute the values into the formula and compute the balance.

\[
A = 2000 \left(1 + \frac{0.0335}{12}\right)^{12 \times 13}
\] 

I'll calculate this.The balance in the account after 13 years is approximately **$3,089.60**.

Would you like more details or have any questions?

Here are five related questions to further explore:
1. How would the balance change if the APR increased to 4%?
2. What if the investment period was only 10 years instead of 13 years?
3. How does quarterly compounding compare to monthly compounding in this scenario?
4. What is the difference between simple and compound interest for the same investment?
5. How would you calculate the interest earned over 13 years?

**Tip:** More frequent compounding (like monthly vs. yearly) generally leads to slightly higher returns because the interest is calculated and added more often.

Use the appropriate compound interest formula to compute the balance in the account after the stated period of time. $2,000 is invested for 13 years with an APR of 3.35% and monthly compounding. The balance in the account after 13 years is ​$ (Round to the nearest cent as​ needed.)

Learn how to calculate compound interest for a $2,000 investment over 13 years with a 3.35% APR and monthly compounding. This detailed solution walks through the compound interest formula and shows how the balance grows to approximately $3,089.60. Ideal for high school students in Grades 10-12.

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