Question

A sum of\( 10,000\) becomes \( 14,400\) on compound interest in \(2\) years. What is the rate of interest per annum?

• A. \(10\%\)
• B. \(40\%\)
• C. \(20\%\)
• D. \(15\%\)

Answer 1

The Correct Option is C

To find the rate of interest per annum when a sum becomes a larger amount via compound interest, we use the compound interest formula:

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

where:

• \( A \) is the final amount,
• \( P \) is the principal amount,
• \( r \) is the rate of interest per annum,
• \( n \) is the number of years.

Given \( A = 14,400 \), \( P = 10,000 \), and \( n = 2 \), we need to find \( r \). Plugging these values into the formula, we have:

\( 14,400 = 10,000 \left(1 + \frac{r}{100}\right)^2 \)

Dividing both sides by \( 10,000 \) gives:

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

Taking the square root on both sides:

\( \sqrt{1.44} = 1 + \frac{r}{100} \)

We know \( \sqrt{1.44} = 1.2 \), so:

\( 1.2 = 1 + \frac{r}{100} \)

Solving for \( r \) gives:

\( \frac{r}{100} = 0.2 \)

Thus, \( r = 20 \).

The rate of interest per annum is \( 20\% \).