Find the compound interest on Rs 10000 for 1 year and 3 months at 8% P.A compounded annually​

To calculate the compound interest, we'll break the calculation into two parts: first for 1 year and then for 3 months. 

### Given:
- Principal (\(P\)) = Rs 10,000
- Rate of Interest (\(r\)) = 8% per annum
- Time (\(t\)) = 1 year and 3 months

Since the interest is compounded annually, the 1 year and 3 months will be treated as 1.25 years (where 3 months is converted to a fraction of a year: \( \frac{3}{12} = 0.25 \)).

### Compound Interest Formula:
\[
A = P \left(1 + \frac{r}{100}\right)^t
\]
\[
\text{Compound Interest} = A - P
\]

### Calculation:

1. Convert the rate and time to the required format:
   - Rate (\(r\)) = 8%
   - Time (\(t\)) = 1.25 years

2. Substitute the values into the formula:
\[
A = 10000 \left(1 + \frac{8}{100}\right)^{1.25}
\]
\[
A = 10000 \left(1.08\right)^{1.25}
\]

Let's calculate this step by step:

\[
A = 10000 \times 1.1038128906 \approx 11038.13
\]

3. Finally, find the compound interest:
\[
\text{Compound Interest} = A - P = 11038.13 - 10000 = Rs 1038.13
\]

### Answer:
The compound interest on Rs 10,000 for 1 year and 3 months at 8% per annum compounded annually is **Rs 1038.13**.

Would you like more details or have any questions?

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Here are five related questions:
1. How would the compound interest change if the interest was compounded semi-annually instead of annually?
2. What would be the compound interest for 2 years at the same rate?
3. How does simple interest differ from compound interest for the same principal, rate, and time?
4. If the time was 2 years and 6 months, how would the calculation change?
5. What would be the total amount after 5 years with the same principal and rate?

**Tip:** For compound interest, understanding how to convert months into years can help in accurate calculations.

Learn how to calculate compound interest on Rs 10,000 at 8% per annum compounded annually for 1 year and 3 months. Detailed step-by-step solution with formulas and calculations provided.

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