If the difference between ST and CI for 2 years is 1.5 at the rate of 5% then find the amount?

Options

A. ₹ 700
B. ₹650
C. ₹ 500
D. ₹600

Answer

To solve the problem of finding the principal amount (P) given that the difference between Simple Interest (SI) and Compound Interest (CI) for 2 years is 1.5 at a rate of 5%, we can follow these steps:

### Step 1: Understand the relationship between SI and CI
The difference between Compound Interest (CI) and Simple Interest (SI) for 2 years can be calculated using the formula:
\[ \text{Difference} = \text{CI} - \text{SI} = \frac{P \times R^2}{100^2} \]
where:
- \( P \) is the principal amount,
- \( R \) is the rate of interest,
- The time period is 2 years.

### Step 2: Set up the equation
From the problem, we know that the difference is 1.5 and the rate (R) is 5%. Therefore, we can set up the equation:
\[ 1.5 = \frac{P \times (5)^2}{100^2} \]

### Step 3: Substitute the values
Substituting the values into the equation:
\[ 1.5 = \frac{P \times 25}{10000} \]

### Step 4: Solve for P
To isolate \( P \), multiply both sides by 10000:
\[ 1.5 \times 10000 = P \times 25 \]
\[ 15000 = P \times 25 \]
Now, divide both sides by 25:
\[ P = \frac{15000}{25} \]
\[ P = 600 \]

### Step 5: Conclusion
Thus, the principal amount \( P \) is 600.

### Final Answer:
The amount (principal) is **600**.

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