The compound interest on Rs. 800 in `2(1)/(2)` years at 5% is

Answer

To find the compound interest on Rs. 800 for 2.5 years at a rate of 5% per annum, we can follow these steps:

### Step 1: Identify the Principal, Rate, and Time
- Principal (P) = Rs. 800
- Rate (R) = 5% per annum = 5/100 = 0.05
- Time (T) = 2.5 years

### Step 2: Calculate the Compound Interest for the First Year
The formula for compound interest for one year is:
\[ \text{Interest} = P \times R \]

For the first year:
\[ \text{Interest}_1 = 800 \times 0.05 = 40 \text{ Rs.} \]

### Step 3: Calculate the Amount at the End of the First Year
The amount at the end of the first year (A1) is:
\[ A_1 = P + \text{Interest}_1 = 800 + 40 = 840 \text{ Rs.} \]

### Step 4: Calculate the Compound Interest for the Second Year
Now, we use the new principal (A1) for the second year:
\[ \text{Interest}_2 = A_1 \times R = 840 \times 0.05 = 42 \text{ Rs.} \]

### Step 5: Calculate the Amount at the End of the Second Year
The amount at the end of the second year (A2) is:
\[ A_2 = A_1 + \text{Interest}_2 = 840 + 42 = 882 \text{ Rs.} \]

### Step 6: Calculate the Compound Interest for the Half Year
For the remaining half year, we again use the new principal (A2):
\[ \text{Interest}_{\text{half}} = A_2 \times R \times \frac{1}{2} = 882 \times 0.05 \times 0.5 = 22.05 \text{ Rs.} \]

### Step 7: Calculate Total Compound Interest
Now, we sum up all the interest amounts:
\[ \text{Total Compound Interest} = \text{Interest}_1 + \text{Interest}_2 + \text{Interest}_{\text{half}} = 40 + 42 + 22.05 = 104.05 \text{ Rs.} \]

### Final Answer
The compound interest on Rs. 800 in 2.5 years at 5% is **Rs. 104.05**.

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