What sum will amount to Rs. 6,600 in 4 years at 8% per annum simple interest?

Options

A. Rs. 6,000
B. Rs. 5,000
C. Rs 4,000
D. Rs 6,200

Answer

To solve the problem of finding the principal amount that will amount to Rs. 6,600 in 4 years at 8% per annum simple interest, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for Amount in Simple Interest:**
The formula for the amount (A) in simple interest is given by:
\[ A = P + SI \]
where \( SI \) (Simple Interest) is calculated using the formula:
\[ SI = \frac{P \times R \times T}{100} \]
Here, \( P \) is the principal, \( R \) is the rate of interest, and \( T \) is the time in years.

2. **Identify the given values:**
- Amount (A) = Rs. 6,600
- Rate (R) = 8%
- Time (T) = 4 years

3. **Set up the equation:**
Substitute the values into the formula for amount:
\[ 6600 = P + \frac{P \times 8 \times 4}{100} \]

4. **Calculate the Simple Interest:**
First, calculate the Simple Interest:
\[ SI = \frac{P \times 8 \times 4}{100} = \frac{32P}{100} \]

5. **Rewrite the equation:**
Substitute \( SI \) back into the amount equation:
\[ 6600 = P + \frac{32P}{100} \]

6. **Combine like terms:**
To combine the terms, convert \( P \) into a fraction with a common denominator:
\[ 6600 = \frac{100P}{100} + \frac{32P}{100} = \frac{132P}{100} \]

7. **Clear the fraction:**
Multiply both sides by 100 to eliminate the denominator:
\[ 6600 \times 100 = 132P \]
\[ 660000 = 132P \]

8. **Solve for P (Principal):**
Divide both sides by 132 to find \( P \):
\[ P = \frac{660000}{132} \]

9. **Calculate the value of P:**
Performing the division:
\[ P = 5000 \]

### Final Answer:
The principal amount is Rs. 5,000.

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