Finance. Suppose that $ 2 comma 200 is invested at 5.5 % annual interest​ rate, compounded monthly. How much money will be in the account in​ (A) 11 ​months? (B) 19 ​years?
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Part 1
​(A) Amount after 11 ​months: ​$
  
enter your response here ​(Round to the nearest​ cent.)

To calculate the amount of money in an account with compound interest, 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 time $ t $,
- $ P $ is the principal amount (initial investment),
- $ r $ is the annual interest rate (in decimal),
- $ n $ is the number of times the interest is compounded per year,
- $ t $ is the time in years.

Given:
- $ P = 2200 $,
- $ r = 5.5\% = 0.055 $,
- $ n = 12 $ (since it's compounded monthly),
- $ t = \frac{11}{12} $ years for Part A (since 11 months is $ \frac{11}{12} $ of a year).

Let's calculate the amount after 11 months.The amount in the account after 11 months will be **$2,313.49**.

Would you like to move on to Part B or ask any questions? Below are some questions that expand on this topic:

1. What would the amount be if the interest were compounded daily instead of monthly?
2. How does changing the interest rate affect the final amount?
3. What is the formula for continuous compounding, and how does it differ from monthly compounding?
4. How does the compounding period affect the total interest earned?
5. What happens to the total amount if the investment duration is reduced to 6 months?

**Tip:** The more frequently interest is compounded, the higher the final amount due to the effect of interest being calculated on previously earned interest.

Finance. Suppose that $ 2,200 is invested at 5.5% annual interest​ rate, compounded monthly. How much money will be in the account in​ (A) 11 ​months? (B) 19 ​years? (A) Amount after 11 ​months: ​$ (Round to the nearest​ cent.)

Learn how to calculate the compound interest on an investment of $2,200 at a 5.5% annual interest rate, compounded monthly. Find out the amount in the account after 11 months and 19 years. This problem uses the compound interest formula A = P(1 + r/n)^(nt) and is suitable for high school students in Grades 10-12.

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