The total amount of ₹ 14,500 with simple interest in 6 years is ₹ 21,460, find out the Rate of interest per annum?

Options

A. `4%`
B. `10%`
C. `6%`
D. `8%`

Answer

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

\[ SI = \frac{P \times R \times T}{100} \]

Where:
- \( SI \) = Simple Interest
- \( P \) = Principal amount (initial amount)
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 1: Identify the given values
- Total Amount (A) = ₹ 21,460
- Principal Amount (P) = ₹ 14,500
- Time (T) = 6 years

### Step 2: Calculate the Simple Interest (SI)
The Simple Interest can be calculated using the formula:

\[ SI = A - P \]

Substituting the values:

\[ SI = 21,460 - 14,500 \]

Calculating:

\[ SI = 6,960 \]

### Step 3: Substitute the values into the SI formula
Now we can substitute the values into the simple interest formula to find the rate of interest \( R \):

\[ 6,960 = \frac{14,500 \times R \times 6}{100} \]

### Step 4: Rearranging the equation to solve for \( R \)
To isolate \( R \), we can rearrange the equation:

\[ R = \frac{6,960 \times 100}{14,500 \times 6} \]

### Step 5: Calculate \( R \)
Now we can calculate \( R \):

\[ R = \frac{696,000}{87,000} \]

Calculating:

\[ R = 8 \]

### Conclusion
The rate of interest per annum is \( 8\% \).

---