An amount invested at simple interest gives Rs 4320 interest at rate of 18% in 4 years. What is the principal (in Rs)?

Options

A. 5000
B. 5500
C. 6000
D. 6500

Answer

To find the principal amount (P) when given the simple interest (SI), rate (R), and time (T), we can use the formula for simple interest:

\[ SI = \frac{P \times R \times T}{100} \]

Given:
- Simple Interest (SI) = Rs 4320
- Rate (R) = 18%
- Time (T) = 4 years

### Step-by-Step Solution:

**Step 1: Write the formula for Simple Interest.**
\[ SI = \frac{P \times R \times T}{100} \]

**Hint:** Remember that SI is calculated based on the principal amount, rate of interest, and time.

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**Step 2: Substitute the known values into the formula.**
\[ 4320 = \frac{P \times 18 \times 4}{100} \]

**Hint:** Make sure to replace SI, R, and T with the values given in the question.

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**Step 3: Simplify the equation.**
\[ 4320 = \frac{72P}{100} \]

**Hint:** Calculate \( 18 \times 4 \) to simplify the equation.

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**Step 4: Eliminate the fraction by multiplying both sides by 100.**
\[ 4320 \times 100 = 72P \]
\[ 432000 = 72P \]

**Hint:** Multiplying by 100 helps to get rid of the denominator.

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**Step 5: Solve for P by dividing both sides by 72.**
\[ P = \frac{432000}{72} \]

**Hint:** Division will help isolate P on one side of the equation.

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**Step 6: Calculate the value of P.**
\[ P = 6000 \]

**Hint:** Perform the division carefully to ensure accuracy.

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**Final Answer:**
The principal amount (P) is Rs 6000.

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