Reeta invested ₹P in a scheme offering simple interest at the rate of `12%` pa. If the difference between the interest earned at the end of three years and that earned at the end of five years was ₹2880, what is the value of ‘P’?

Options

A. ₹ 9000
B. ₹ 10800
C. ₹ 12000
D. ₹ 15000

Answer

To find the value of 'P' in the given problem, we will follow these steps:

### Step 1: Understand the formula for Simple Interest
The formula for calculating Simple Interest (SI) is given by:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount (the initial amount of money)
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 2: Calculate Simple Interest for 3 years
For 3 years, the Simple Interest earned can be calculated as:
\[ SI_3 = \frac{P \times 12 \times 3}{100} = \frac{36P}{100} = \frac{18P}{50} \]

### Step 3: Calculate Simple Interest for 5 years
For 5 years, the Simple Interest earned can be calculated as:
\[ SI_5 = \frac{P \times 12 \times 5}{100} = \frac{60P}{100} = \frac{30P}{50} \]

### Step 4: Find the difference between the two interests
According to the problem, the difference between the interest earned at the end of 5 years and that earned at the end of 3 years is ₹2880. Therefore, we can set up the equation:
\[ SI_5 - SI_3 = 2880 \]
Substituting the values we calculated:
\[ \frac{60P}{100} - \frac{36P}{100} = 2880 \]

### Step 5: Simplify the equation
Now, simplify the left side of the equation:
\[ \frac{60P - 36P}{100} = 2880 \]
\[ \frac{24P}{100} = 2880 \]

### Step 6: Solve for P
To isolate \( P \), multiply both sides by 100:
\[ 24P = 2880 \times 100 \]
\[ 24P = 288000 \]
Now, divide both sides by 24:
\[ P = \frac{288000}{24} \]
\[ P = 12000 \]

### Final Answer
The value of \( P \) is ₹12,000.

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