Certainly! Let's break down the solution step-by-step to find the simple interest for 1200 rupees at a rate of 2 paisa per rupee per month over 2 months.
### Step 1: Understanding the Given Values
1. Principal Amount (P): 1200 rupees
2. Rate of Interest: 2 paisa per rupee per month
3. Time: 2 months
### Step 2: Conversion of Rate of Interest
The given interest rate is 2 paisa per rupee per month.
- There are 100 paisa in a rupee.
- To convert the rate to an annual percentage rate, we first convert the rate to a monthly percentage by multiplying by 12 (since there are 12 months in a year) and divide by 100 to account for the paisa-to-rupee conversion.
Rate per year in percentage:
[tex]\[ \text{Rate (annual)} = 2 \times 12 / 100 = 0.24\% \text{ per year} \][/tex]
### Step 3: Convert Time from Months to Years
The given time is 2 months. To convert months to years, we divide by 12 (since there are 12 months in a year).
[tex]\[ \text{Time (years)} = \frac{2}{12} = \frac{1}{6} \text{ years} \][/tex]
### Step 4: Calculate Simple Interest (SI)
The formula for Simple Interest (SI) is given by:
[tex]\[ \text{SI} = \frac{P \times R \times T}{100} \][/tex]
where,
- [tex]\(P\)[/tex] is the principal amount (1200 rupees),
- [tex]\(R\)[/tex] is the annual rate of interest (0.24%),
- [tex]\(T\)[/tex] is the time in years ([tex]\(\frac{1}{6}\)[/tex]).
Substitute the values into the formula:
[tex]\[ \text{SI} = \frac{1200 \times 0.24 \times \frac{1}{6}}{100} \][/tex]
[tex]\[ \text{SI} = \frac{1200 \times 0.24 \times 0.16666666666666666}{100} \][/tex]
[tex]\[ \text{SI} = \frac{48}{100} = 0.48 \text{ rupees} \][/tex]
### Conclusion
The simple interest for a principal of 1200 rupees at a rate of 2 paisa per rupee per month over a period of 2 months is [tex]\( \text{0.48 rupees} \)[/tex].
