The compound interest on Rs. 4000 at 25% p.a. in 3 years :

Options

A. 1235
B. 5625
C. 3812.5
D. 3750.5

Answer

To find the compound interest on Rs. 4000 at a rate of 25% per annum over a period of 3 years, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 4000
- Rate (R) = 25% per annum
- Time (T) = 3 years

### Step 2: Use the compound interest formula
The formula for the amount (A) after time T with compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ A = 4000 \left(1 + \frac{25}{100}\right)^3 \]

### Step 4: Simplify the expression inside the parentheses
\[ A = 4000 \left(1 + 0.25\right)^3 \]
\[ A = 4000 \left(1.25\right)^3 \]

### Step 5: Calculate \( (1.25)^3 \)
Calculating \( (1.25)^3 \):
\[ (1.25)^3 = 1.25 \times 1.25 \times 1.25 \]
\[ = 1.5625 \]

### Step 6: Calculate the amount (A)
Now substitute back to find A:
\[ A = 4000 \times 1.5625 \]
\[ A = 6250 \]

### Step 7: Calculate the compound interest (CI)
The compound interest is given by:
\[ CI = A - P \]
\[ CI = 6250 - 4000 \]
\[ CI = 2250 \]

### Final Answer
The compound interest on Rs. 4000 at 25% p.a. in 3 years is Rs. 2250.

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