Same principal is invested in schemes of compound interest and simple interest. The interest obtained in simple interest and compound interest schemes after 2 years are Rs 1200 and Rs 1290 respectively. If the rate of interest is 15%, then what is the principal (in Rs)?

Options

A. 4000
B. 6000
C. 2500
D. 3000

Answer

To solve the problem step by step, we need to find the principal amount (P) given the simple interest (SI) and compound interest (CI) earned after 2 years, along with the rate of interest.

### Step 1: Calculate the Simple Interest for 2 Years
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(P\) = Principal amount
- \(R\) = Rate of interest per annum
- \(T\) = Time in years

Given:
- \(SI = 1200\)
- \(R = 15\%\)
- \(T = 2\)

Substituting the values into the formula:
\[ 1200 = \frac{P \times 15 \times 2}{100} \]

### Step 2: Simplify the Equation
\[ 1200 = \frac{30P}{100} \]
\[ 1200 = 0.3P \]

### Step 3: Solve for Principal (P)
To find \(P\), divide both sides by 0.3:
\[ P = \frac{1200}{0.3} \]
\[ P = 4000 \]

### Step 4: Verify with Compound Interest
Now, let's verify with Compound Interest (CI). The formula for Compound Interest after 2 years is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
Substituting the values:
\[ CI = 4000 \left(1 + \frac{15}{100}\right)^2 - 4000 \]
\[ = 4000 \left(1.15\right)^2 - 4000 \]
\[ = 4000 \times 1.3225 - 4000 \]
\[ = 5290 - 4000 \]
\[ = 1290 \]

This confirms that the CI is indeed Rs. 1290.

### Conclusion
Thus, the principal amount is:
\[ \boxed{4000} \]