A sum of Rs. 8,000 is invested for 2 years at 10% per annum compound interest. Calculate :
principal for the second year.

Answer

To solve the problem of finding the principal for the second year when a sum of Rs. 8,000 is invested for 2 years at 10% per annum compound interest, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Principal (P) = Rs. 8,000
- Rate of Interest (r) = 10% per annum
- Time (n) = 1 year (since we are calculating for the first year)

2. **Use the Compound Interest Formula:**
The formula for calculating the amount (A) at the end of the investment period is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]

3. **Substitute the Values for the First Year:**
\[ A = 8000 \left(1 + \frac{10}{100}\right)^1 \]
Simplifying the expression inside the parentheses:
\[ A = 8000 \left(1 + 0.1\right)^1 = 8000 \left(1.1\right)^1 \]

4. **Calculate the Amount at the End of the First Year:**
\[ A = 8000 \times 1.1 = 8000 \times \frac{11}{10} \]
\[ A = 8800 \]
So, the amount at the end of the first year is Rs. 8,800.

5. **Determine the Principal for the Second Year:**
The amount at the end of the first year (Rs. 8,800) becomes the principal for the second year. Therefore:
\[ \text{Principal for the second year} = Rs. 8,800 \]

### Final Answer:
The principal for the second year is Rs. 8,800.