Calculating Simple Interest Time Period

The question asks us to determine the time required for a principal amount to grow and yield a specific simple interest amount at a given annual rate.

We are given the following information:

• Principal Amount (P) = Rs. 450
• Simple Interest (SI) = Rs. 81
• Rate of Interest (R) = 4.5% per annum
• Time (T) = ? (We need to find this)

The formula for calculating Simple Interest is:

\( \text{SI} = \frac{P \times R \times T}{100} \)

To find the Time (T), we can rearrange the formula:

\( T = \frac{\text{SI} \times 100}{P \times R} \)

Now, let's substitute the given values into the formula:

\( T = \frac{81 \times 100}{450 \times 4.5} \)

Let's perform the calculation step-by-step:

1. Multiply the Simple Interest by 100: \( 81 \times 100 = 8100 \)
2. Multiply the Principal by the Rate: \( 450 \times 4.5 \)

To calculate \( 450 \times 4.5 \):

\( 450 \times 4.5 = 450 \times \left(4 + 0.5\right) = \left(450 \times 4\right) + \left(450 \times 0.5\right) \)

\( 450 \times 4 = 1800 \)

\( 450 \times 0.5 = 225 \)

\( 1800 + 225 = 2025 \)

So, \( 450 \times 4.5 = 2025 \).

Now, put these values back into the formula for T:

\( T = \frac{8100}{2025} \)

To simplify the fraction \( \frac{8100}{2025} \), we can divide both the numerator and denominator by common factors. Let's try dividing by 25:

\( 8100 \div 25 = 324 \)

\( 2025 \div 25 = 81 \)

So, \( T = \frac{324}{81} \).

Now, we divide 324 by 81:

\( 324 \div 81 \)

We know that \( 81 \times 4 = 324 \).

So, \( T = 4 \).

Since the rate is given as per annum, the time is in years.

Therefore, it will take 4 years for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum simple interest.