On what principal will the simple interest be Rs. 7,008 in 6 years 3 months at 5% per year ?

Answer

To find the principal amount on which the simple interest will be Rs. 7,008 in 6 years and 3 months at a rate of 5% per annum, we can follow these steps:

### Step 1: Identify the given values
- Simple Interest (SI) = Rs. 7,008
- Time (T) = 6 years and 3 months
- Rate of Interest (R) = 5% per annum

### Step 2: Convert the time into years
The time given is 6 years and 3 months. We need to convert the 3 months into years:
- 3 months = 3/12 years = 1/4 years

Now, add this to the 6 years:
- T = 6 + 1/4 = 6.25 years or T = 25/4 years

### Step 3: Use the formula for Simple Interest
The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- SI = Simple Interest
- P = Principal
- R = Rate of Interest
- T = Time in years

### Step 4: Substitute the known values into the formula
We know:
- SI = 7,008
- R = 5%
- T = 25/4 years

Substituting these values into the formula:
\[ 7008 = \frac{P \times 5 \times \frac{25}{4}}{100} \]

### Step 5: Simplify the equation
First, simplify the fraction:
\[ 7008 = \frac{P \times 5 \times 25}{400} \]

Now, multiply both sides by 400 to eliminate the fraction:
\[ 7008 \times 400 = P \times 5 \times 25 \]

Calculating the left side:
\[ 7008 \times 400 = 2803200 \]

So, we have:
\[ 2803200 = P \times 125 \]

### Step 6: Solve for P (Principal)
Now, divide both sides by 125 to find P:
\[ P = \frac{2803200}{125} \]

Calculating this gives:
\[ P = 22425.6 \]

### Conclusion
The principal amount is Rs. 22,425.6.

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