Simple interest on a sum of Rs 50200 for 3 months is Rs 1380.5. What is the rate (in percentage) of interest per annum?

Options

A. 11
B. 9
C. 9.5
D. 8.5

Answer

To find the rate of interest per annum, we can use the formula for simple interest:

\[ \text{Simple Interest (SI)} = \frac{P \times R \times T}{100} \]

Where:
- \( P \) = Principal amount (the initial sum of money)
- \( R \) = Rate of interest per annum
- \( T \) = Time (in years)

Given:
- Principal \( P = 50200 \)
- Simple Interest \( SI = 1380.5 \)
- Time \( T = 3 \text{ months} = \frac{3}{12} = \frac{1}{4} \text{ years} \)

We need to find the rate \( R \).

### Step 1: Substitute the known values into the formula

\[ 1380.5 = \frac{50200 \times R \times \frac{1}{4}}{100} \]

### Step 2: Simplify the equation

Multiply both sides by 100 to eliminate the fraction:

\[ 138050 = 50200 \times R \times \frac{1}{4} \]

### Step 3: Multiply both sides by 4 to isolate \( R \)

\[ 552200 = 50200 \times R \]

### Step 4: Solve for \( R \)

Divide both sides by 50200:

\[ R = \frac{552200}{50200} \]

### Step 5: Calculate \( R \)

\[ R = 11 \]

### Conclusion

The rate of interest per annum is \( 11\% \).

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