A sum of ₹ 10000 is lent on simple interest at the rate of 15% per annum. What is the difference between Simple interest for 6 years and the simple interest for 2 years?

Options

A. ₹4000
B. ₹8000
C. ₹6000
D. ₹4500

Answer

To solve the problem step by step, we will calculate the simple interest for both 6 years and 2 years, and then find the difference between the two.

### Step 1: Identify the given values
- Principal (P) = ₹10,000
- Rate of interest (R) = 15% per annum
- Time for the first calculation (T1) = 6 years
- Time for the second calculation (T2) = 2 years

### Step 2: Calculate Simple Interest for 6 years
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the values for 6 years:
\[ SI_{6} = \frac{10,000 \times 15 \times 6}{100} \]
Calculating this:
\[ SI_{6} = \frac{10,000 \times 90}{100} = \frac{900,000}{100} = ₹9,000 \]

### Step 3: Calculate Simple Interest for 2 years
Now, substituting the values for 2 years:
\[ SI_{2} = \frac{10,000 \times 15 \times 2}{100} \]
Calculating this:
\[ SI_{2} = \frac{10,000 \times 30}{100} = \frac{300,000}{100} = ₹3,000 \]

### Step 4: Find the difference between the two Simple Interests
Now, we find the difference:
\[ \text{Difference} = SI_{6} - SI_{2} \]
Substituting the values we calculated:
\[ \text{Difference} = 9,000 - 3,000 = ₹6,000 \]

### Final Answer
The difference between the Simple Interest for 6 years and the Simple Interest for 2 years is ₹6,000.

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