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

Answer

To calculate the interest for the second year on a sum of Rs. 8,000 invested at a 10% per annum compound interest rate, we can follow these steps:

### Step 1: Identify the Principal, Rate, and Time for the First Year
- **Principal (P)** = Rs. 8,000
- **Rate (R)** = 10% per annum
- **Time (T)** = 1 year

### Step 2: Calculate the Amount at the End of the First Year
We use the formula for compound interest to find the amount after the first year:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Substituting the values:
\[ A = 8000 \left(1 + \frac{10}{100}\right)^1 \]
\[ A = 8000 \left(1 + 0.1\right)^1 \]
\[ A = 8000 \times 1.1 \]
\[ A = 8800 \]
So, the amount at the end of the first year is Rs. 8,800.

### Step 3: Identify the Principal, Rate, and Time for the Second Year
Now, the amount at the end of the first year becomes the principal for the second year:
- **Principal (P)** = Rs. 8,800
- **Rate (R)** = 10% per annum
- **Time (T)** = 1 year

### Step 4: Calculate the Interest for the Second Year
We can calculate the interest for the second year using the formula:
\[ \text{Interest} = P \times R \times T \div 100 \]
Substituting the values:
\[ \text{Interest} = 8800 \times 10 \times 1 \div 100 \]
\[ \text{Interest} = 8800 \times 10 \div 100 \]
\[ \text{Interest} = 8800 \div 10 \]
\[ \text{Interest} = 880 \]
Thus, the interest for the second year is Rs. 880.

### Summary of the Solution
- Amount at the end of the first year = Rs. 8,800
- Interest for the second year = Rs. 880

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