The question asks for the rate of compound interest given the principal amount, the final amount, and the time period.

Compound Interest Calculation

We use the formula for compound interest:

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

Where:

• $A$ = Amount (₹1,440)
• $P$ = Principal (₹1,000)
• $r$ = Rate of interest per annum (%)
• $n$ = Number of years (2)

Solving for the Interest Rate (r)

Substitute the given values into the formula:

$ 1440 = 1000 \left(1 + \frac{r}{100}\right)^2 $

Divide both sides by the principal amount (1000):

$ \frac{1440}{1000} = \left(1 + \frac{r}{100}\right)^2 $

$ 1.44 = \left(1 + \frac{r}{100}\right)^2 $

Take the square root of both sides:

$ \sqrt{1.44} = 1 + \frac{r}{100} $

$ 1.2 = 1 + \frac{r}{100} $

Subtract 1 from both sides:

$ 1.2 - 1 = \frac{r}{100} $

$ 0.2 = \frac{r}{100} $

Multiply by 100 to find the rate:

$ r = 0.2 \times 100 $

$ r = 20 $

Therefore, the rate of compound interest is 20%.