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.