Question

A sum of money becomes double in R years at an annual rate of simple interest. What is the annual rate of interest?

• A. 9%
• B. 10%
• C. 12%
• D. 7%

Hint:

For a sum to double in simple interest, the rate of interest is given by \( \frac{100}{T} \), where \( T \) is the time in years.

Answer 1

The Correct Option is B

Let the sum of money be \( P \) and the amount after \( R \) years be \( 2P \) (since the sum doubles). The formula for simple interest is: \[ \text{Simple Interest} = \frac{P \times R \times T}{100}, \] where \( P \) is the principal, \( R \) is the rate of interest, and \( T \) is the time in years. Since the amount doubles, the simple interest is equal to the principal amount: \[ \text{Simple Interest} = P. \] Substitute in the formula: \[ P = \frac{P \times R \times R}{100} \quad \Rightarrow \quad 100 = R^2 \quad \Rightarrow \quad R = 10. \] Thus, the annual rate of interest is 10%, corresponding to option (2).