Compound Interest Rate Calculation

This solution explains how to calculate the rate of interest when the amount, principal, and time period (compounded yearly) are given.

Compound Interest Formula

The formula for the amount (A) when compounded yearly is:

$ A = P \left(1 + \frac{R}{100}\right)^T $

Where:

• A = Amount
• P = Principal
• R = Rate of interest per year (%)
• T = Time period in years

Given Values

From the question, we have:

• Amount ($A$) = Rs. 600
• Principal ($P$) = Rs. 450
• Time ($T$) = 1 year

Calculation Steps

Since the time period ($T$) is 1 year, the formula simplifies to:

$ A = P \left(1 + \frac{R}{100}\right) $

Substitute the given values into the simplified formula:

$ 600 = 450 \left(1 + \frac{R}{100}\right) $

Now, solve for the rate ($R$):

1. Divide both sides by the Principal (450):

   $ \frac{600}{450} = 1 + \frac{R}{100} $

2. Simplify the fraction $\frac{600}{450}$:

   $ \frac{4}{3} = 1 + \frac{R}{100} $

3. Subtract 1 from both sides to isolate $\frac{R}{100}$:

   $ \frac{4}{3} - 1 = \frac{R}{100} $

   $ \frac{1}{3} = \frac{R}{100} $

4. Multiply both sides by 100 to find the rate ($R$):

   $ R = \frac{1}{3} \times 100 $

   $ R = 33.33... \% $

Final Rate of Interest

The calculated rate of interest is 33.33%.