calculate the amount and compound interest on Rs. 9600 for 1121 \frac{1}{2}121​ years at 8% per annum compounded half-yearly. Class 8 base

To calculate the compound interest and amount on Rs. 9600 over \(12\frac{1}{2}\) years at an 8% annual interest rate, compounded half-yearly, we will use the following formula for compound interest when compounding occurs more frequently than annually:

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

where:
- \( P = 9600 \) (principal),
- \( r = 8\% \) (annual interest rate),
- \( n = 2 \) (since interest is compounded half-yearly, there are 2 compounding periods per year),
- \( t = 12.5 \) years.

### Step-by-Step Solution:

1. **Convert the annual rate to half-yearly rate:**
   \[
   \text{Half-yearly rate} = \frac{8\%}{2} = 4\%
   \]

2. **Calculate the total number of compounding periods:**
   \[
   \text{Number of periods} = n \times t = 2 \times 12.5 = 25
   \]

3. **Apply the values to the compound interest formula:**
   \[
   A = 9600 \left(1 + \frac{4}{100}\right)^{25}
   \]
   Simplify the inside of the parentheses:
   \[
   A = 9600 \left(1.04\right)^{25}
   \]

4. **Calculate \( \left(1.04\right)^{25} \):**

   \( 1.04^{25} \approx 2.6658 \).

5. **Find the final amount \( A \):**
   \[
   A = 9600 \times 2.6658 = 25591.68
   \]

6. **Calculate the compound interest \( CI \):**
   \[
   CI = A - P = 25591.68 - 9600 = 15991.68
   \]

### Final Answer
- **Amount (A)**: Rs. 25,591.68
- **Compound Interest (CI)**: Rs. 15,991.68

Would you like further details or have any questions?

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### Related Practice Questions

1. Calculate the compound interest on Rs. 10,000 for 10 years at 10% per annum compounded quarterly.
2. What would be the amount on Rs. 5,000 for 3 years at 6% per annum compounded annually?
3. If Rs. 15,000 is invested at 12% per annum compounded monthly for 5 years, find the compound interest.
4. Calculate the final amount on Rs. 8,000 for 7 years at 5% per annum compounded half-yearly.
5. Find the compound interest on Rs. 20,000 for 4 years at 10% per annum compounded semi-annually.

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**Tip:** For compound interest problems, break down each variable first (like rate per period and number of compounding periods) to simplify calculations.

Calculate the amount and compound interest on Rs. 9600 for 12.5 years at 8% per annum compounded half-yearly.

Learn how to calculate the compound interest and final amount on an investment of Rs. 9600 for 12.5 years at an 8% annual interest rate, compounded half-yearly. This step-by-step solution covers the compound interest formula, calculating half-yearly compounding periods, and finding the effective interest rate. Ideal for Grade 8 math students.

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