The compound interest on Rs 2800 for `1(1/2)` years at 10% per annum is -

Options

A. Rs 434
B. Rs 436.75
C. Rs 441.35
D. Rs 420

Answer

To find the compound interest on Rs 2800 for 1.5 years at a rate of 10% per annum, we can follow these steps:

### Step 1: Identify the Variables
- Principal (P) = Rs 2800
- Rate of Interest (R) = 10%
- Time (T) = 1.5 years (which can be expressed as 1 year and 6 months)

**Hint:** Make sure to convert mixed numbers into improper fractions for easier calculations.

### Step 2: Calculate the Amount for the First Year
Using the formula for simple interest for the first year:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
For the first year:
\[ \text{SI} = \frac{2800 \times 10 \times 1}{100} = 280 \text{ Rs} \]

**Hint:** Remember that for the first year, the interest is calculated using the full principal amount.

### Step 3: Calculate the Amount After the First Year
The total amount after the first year is:
\[ A_1 = P + \text{SI} = 2800 + 280 = 3080 \text{ Rs} \]

**Hint:** Always add the interest to the principal to find the new amount.

### Step 4: Calculate the Interest for the Next Half Year
For the next half year (0.5 years), we will calculate the interest on the new principal amount (A_1):
\[ \text{SI}_{\text{half}} = \frac{A_1 \times R \times T}{100} \]
\[ \text{SI}_{\text{half}} = \frac{3080 \times 10 \times 0.5}{100} = 154 \text{ Rs} \]

**Hint:** When calculating interest for a fraction of a year, adjust the time accordingly.

### Step 5: Calculate Total Compound Interest
Now, we can find the total compound interest by adding the interest from the first year and the interest from the half year:
\[ \text{CI} = \text{SI} + \text{SI}_{\text{half}} = 280 + 154 = 434 \text{ Rs} \]

**Hint:** Compound interest is the sum of all interest earned over the period, including interest on interest.

### Final Answer
The compound interest on Rs 2800 for 1.5 years at 10% per annum is Rs 434.

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