Armaan took 5000 on loan from a bank at the rate of r % p.a. simple interest. After 6 years, he had to pay Rs. 5400 interest. Find the value of r.

Options

A. `20%`
B. `12%`
C. `16%`
D. `18%`

Answer

To find the value of \( r \) (the rate of interest), we can use the formula for simple interest:

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

Where:
- \( P \) is the principal amount (the initial amount of money)
- \( r \) is the rate of interest per annum
- \( t \) is the time in years

Given:
- \( P = 5000 \)
- \( SI = 5400 \)
- \( t = 6 \)

We need to find \( r \).

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

\[ 5400 = \frac{5000 \times r \times 6}{100} \]

### Step 2: Simplify the equation

To eliminate the fraction, we can multiply both sides by 100:

\[ 5400 \times 100 = 5000 \times r \times 6 \]

This gives us:

\[ 540000 = 5000 \times r \times 6 \]

### Step 3: Divide both sides by \( 5000 \times 6 \)

First, calculate \( 5000 \times 6 \):

\[ 5000 \times 6 = 30000 \]

Now, divide both sides by 30000:

\[ r = \frac{540000}{30000} \]

### Step 4: Simplify the division

\[ r = 18 \]

### Conclusion

The value of \( r \) is \( 18\% \).