A sum of money invested at compound interest amounts to Rs. 650 at the end of first year and Rs. 676 at the end of second year. The sum of money is:

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the Given Information
We know that:
- Amount at the end of the first year (A1) = Rs. 650
- Amount at the end of the second year (A2) = Rs. 676

### Step 2: Calculate the Interest Earned in the Second Year
The interest earned in the second year can be calculated by subtracting the amount at the end of the first year from the amount at the end of the second year:
\[ \text{Interest for second year} = A2 - A1 = 676 - 650 = Rs. 26 \]

### Step 3: Calculate the Rate of Interest
The interest earned in the second year is based on the amount at the end of the first year (A1). We can use the formula for interest:
\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]
Here, the Principal for the second year is Rs. 650, and the interest earned is Rs. 26. We can express the rate as a percentage:
\[ \text{Rate} = \frac{\text{Interest}}{\text{Principal}} \times 100 = \frac{26}{650} \times 100 \]
Calculating this gives:
\[ \text{Rate} = \frac{26}{650} \times 100 = 4\% \]

### Step 4: Calculate the Principal Amount
Now that we know the rate of interest is 4%, we can find the principal amount (P). The amount at the end of the first year can be expressed as:
\[ A1 = P + \text{Interest for first year} \]
The interest for the first year can be calculated as:
\[ \text{Interest for first year} = P \times \frac{4}{100} = 0.04P \]
So, we can write:
\[ 650 = P + 0.04P \]
This simplifies to:
\[ 650 = 1.04P \]
Now, we can solve for P:
\[ P = \frac{650}{1.04} \]
Calculating this gives:
\[ P = 625 \]

### Final Answer
The sum of money (Principal) is Rs. 625.

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