Find the amount of Rs. 2500 invested at 12% during the period from `4^(th)` February , 2005 to 18 April 2005 :

Options

A. Rs . 3000
B. Rs. 3800
C. Rs. 2560
D. Rs. 2600

Answer

To find the amount of Rs. 2500 invested at 12% from 4th February 2005 to 18th April 2005, we will follow these steps:

### Step 1: Identify the Principal, Rate, and Time
- **Principal (P)** = Rs. 2500
- **Rate (R)** = 12%
- **Time (T)** = From 4th February 2005 to 18th April 2005

### Step 2: Calculate the Time Period in Days
- **Days in February** = 28 days (since 2005 is not a leap year)
- **Days from 4th February to 28th February** = 28 - 4 = 24 days
- **Days in March** = 31 days
- **Days in April** = 18 days
- **Total Days** = 24 (February) + 31 (March) + 18 (April) = 73 days

### Step 3: Convert Days to Years
- **Number of Days in a Year** = 365 days
- **Time in Years (T)** = 73 / 365 = 0.2 years (approximately)

### Step 4: Calculate the Amount using Compound Interest Formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- \( A \) = Amount
- \( P \) = Principal
- \( R \) = Rate of interest
- \( T \) = Time in years

Substituting the values:
\[ A = 2500 \left(1 + \frac{12}{100}\right)^{0.2} \]
\[ A = 2500 \left(1 + 0.12\right)^{0.2} \]
\[ A = 2500 \left(1.12\right)^{0.2} \]

### Step 5: Calculate \( (1.12)^{0.2} \)
Using a calculator:
\[ (1.12)^{0.2} \approx 1.023 \]

### Step 6: Calculate the Final Amount
Now substituting back into the amount formula:
\[ A \approx 2500 \times 1.023 \]
\[ A \approx 2557.50 \]

### Final Answer
The amount after investing Rs. 2500 at 12% from 4th February 2005 to 18th April 2005 is approximately **Rs. 2557.50**.

---