Jane invested `₹2400` in a scheme offering compound interest at R% pa and earns an interest of `₹504` at end of two years. How much interest she would have earned if she invested the same sum @` (R+5)%`pa simple interest in 2 years

Options

A. `₹720`
B. `₹900`
C. `₹1200`
D. `₹820`

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the Problem
Jane invested ₹2400 in a scheme offering compound interest at R% per annum and earned ₹504 at the end of two years. We need to find out how much interest she would earn if she invested the same amount at (R + 5)% per annum as simple interest for 2 years.

### Step 2: Calculate the Total Amount from Compound Interest
The total amount (A) after 2 years with compound interest can be calculated as:
\[ A = P + CI \]
Where:
- \( P = ₹2400 \) (Principal)
- \( CI = ₹504 \) (Compound Interest)

So,
\[ A = 2400 + 504 = ₹2904 \]

### Step 3: Use the Compound Interest Formula
The formula for compound interest is given by:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
Where:
- \( n = 2 \) (number of years)

Substituting the values we have:
\[ 2904 = 2400 \left(1 + \frac{R}{100}\right)^2 \]

### Step 4: Simplify the Equation
Dividing both sides by 2400:
\[ \frac{2904}{2400} = \left(1 + \frac{R}{100}\right)^2 \]
Calculating the left side:
\[ \frac{2904}{2400} = 1.21 \]

### Step 5: Take the Square Root
Taking the square root of both sides:
\[ \sqrt{1.21} = 1 + \frac{R}{100} \]
Calculating the square root:
\[ 1.1 = 1 + \frac{R}{100} \]

### Step 6: Solve for R
Subtracting 1 from both sides:
\[ 0.1 = \frac{R}{100} \]
Multiplying both sides by 100:
\[ R = 10\% \]

### Step 7: Calculate the New Rate
Now, we need to find the new rate:
\[ R + 5 = 10 + 5 = 15\% \]

### Step 8: Calculate Simple Interest
Using the simple interest formula:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P = ₹2400 \)
- \( R = 15\% \)
- \( T = 2 \) years

Substituting the values:
\[ SI = \frac{2400 \times 15 \times 2}{100} \]

### Step 9: Calculate the Simple Interest
Calculating:
\[ SI = \frac{2400 \times 30}{100} = \frac{72000}{100} = ₹720 \]

### Final Answer
Thus, the interest Jane would have earned if she invested the same sum at (R + 5)% per annum as simple interest in 2 years is:
\[ \text{Simple Interest} = ₹720 \]