A sum of Rs 4200 becomes Rs 5082 in 3 years rate simple interest. What is the rate of interest per annum?

Options

A. `8%`
B. `9%`
C. `5%`
D. `7%`

Answer

To find the rate of interest per annum, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs 4200
- Amount (A) = Rs 5082
- Time (T) = 3 years

### Step 2: Calculate the Simple Interest (SI)
The formula for Simple Interest is:
\[ \text{SI} = \text{Amount} - \text{Principal} \]
Substituting the values:
\[ \text{SI} = 5082 - 4200 = 882 \]

### Step 3: Use the Simple Interest formula to find the rate (R)
The formula for Simple Interest is also given by:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
We can rearrange this formula to solve for R:
\[ R = \frac{\text{SI} \times 100}{P \times T} \]

### Step 4: Substitute the known values into the formula
Substituting the values we have:
\[ R = \frac{882 \times 100}{4200 \times 3} \]

### Step 5: Simplify the equation
Calculating the denominator:
\[ 4200 \times 3 = 12600 \]
Now substituting this back into the equation:
\[ R = \frac{88200}{12600} \]

### Step 6: Perform the division
Calculating:
\[ R = 7 \]

### Conclusion
The rate of interest per annum is:
\[ R = 7\% \]