In how many year interest of Rs. 3000 will be Rs. 1080 at the simple interest rate of `12%` annually ?

Options

A. 3 yr
B. `2(1)/(2)` yr
C. 2 yr
D. `3(1)/(2)` yr

Answer

To find out how many years it will take for the interest on Rs. 3000 to amount to Rs. 1080 at a simple interest rate of 12% 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 (initial investment)
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

Given:
- \( P = 3000 \)
- \( SI = 1080 \)
- \( R = 12 \)

We need to find \( T \).

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

We can rearrange the formula to solve for \( T \):

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

Substituting the values we have:

\[ T = \frac{1080 \times 100}{3000 \times 12} \]

### Step 2: Calculate the denominator

First, calculate \( 3000 \times 12 \):

\[ 3000 \times 12 = 36000 \]

### Step 3: Calculate the entire expression

Now substitute this back into the equation for \( T \):

\[ T = \frac{108000}{36000} \]

### Step 4: Simplify the fraction

Now, simplify \( \frac{108000}{36000} \):

\[ T = 3 \]

### Conclusion

Thus, the time period \( T \) is 3 years.