If principal amount is 10,000 with interest rate of 24% per annum, calculate compound interest for 2 years and 6 months

To calculate the compound interest for 2 years and 6 months, we will use the compound interest formula:

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

Where:
- \( A \) is the amount of money accumulated after interest.
- \( P \) is the principal amount (10,000).
- \( r \) is the annual interest rate (24% or 0.24).
- \( n \) is the number of times the interest is compounded per year (assume it is compounded annually, \( n = 1 \)).
- \( t \) is the time the money is invested (2.5 years or 2 years and 6 months).

Now, let's plug in the values and calculate:

\[
A = 10,000 \left(1 + \frac{0.24}{1}\right)^{1 \times 2.5}
\]
\[
A = 10,000 \left(1.24\right)^{2.5}
\]

First, we'll calculate \( (1.24)^{2.5} \), and then the final value of \( A \). The compound interest is found by subtracting the principal from the final amount \( A - P \).

Let's calculate it:The total amount after 2 years and 6 months is approximately \( 17,121.99 \). 

The compound interest earned is approximately \( 7,121.99 \).

Would you like further details on the calculation, or do you have any questions?

Here are 5 related questions for further exploration:
1. How would the result change if the interest was compounded quarterly instead of annually?
2. What would be the compound interest for 5 years at the same rate?
3. How does the compound interest formula differ from the simple interest formula?
4. What would happen if the interest rate was 12% instead of 24%?
5. How can you calculate the continuous compound interest?

**Tip**: The more frequently interest is compounded, the higher the final amount will be!

If principal amount is 10,000 with interest rate of 24% per annum, calculate compound interest for 2 years and 6 months.

Learn how to calculate compound interest for a principal of 10,000 at a 24% annual interest rate over 2 years and 6 months. This detailed solution involves key financial math concepts such as compound interest, exponents, and percentage. Suitable for students in Grades 9-12.

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