What sum (in Rs) will amount to Rs 6900 in 5 years at simple interest at the rate of 3%?

Options

A. 5250
B. 6800
C. 6000
D. 6300

Answer

To solve the problem of finding the principal sum (P) that will amount to Rs 6900 in 5 years at a simple interest rate of 3%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Simple Interest:**
The formula for the total amount (A) at the end of the time period when simple interest is applied is:
\[ A = P + SI \]
where \( SI \) (Simple Interest) is calculated using the formula:
\[ SI = \frac{P \times R \times T}{100} \]
Here, \( R \) is the rate of interest, and \( T \) is the time in years.

2. **Identify the Given Values:**
- Total Amount (A) = Rs 6900
- Rate of Interest (R) = 3%
- Time (T) = 5 years

3. **Substitute the Values into the Simple Interest Formula:**
First, we need to express the total amount in terms of the principal:
\[ A = P + \frac{P \times R \times T}{100} \]
Substituting the known values:
\[ 6900 = P + \frac{P \times 3 \times 5}{100} \]

4. **Simplify the Equation:**
Calculate the simple interest part:
\[ \frac{3 \times 5}{100} = \frac{15}{100} = 0.15 \]
Therefore, the equation becomes:
\[ 6900 = P + 0.15P \]
Combine like terms:
\[ 6900 = 1.15P \]

5. **Solve for P:**
To find P, divide both sides by 1.15:
\[ P = \frac{6900}{1.15} \]
Calculate the value:
\[ P = 6000 \]

### Conclusion:
The principal sum (P) that will amount to Rs 6900 in 5 years at a simple interest rate of 3% is Rs 6000.