The simple interest earned on a certain amount is double the money when…

Concept

Simple interest is given by SI = (P x R x T) / 100, where P is the principal, R is the annual rate of interest (%), and T is the time in years. Rearranging for the rate gives R = (100 x SI) / (P x T).

Application

1. The interest earned equals double the principal, so SI = 2P.

2. The time given is T = 15 years.

3. Substitute into R = (100 x SI) / (P x T): R = (100 x 2P) / (P x 15) = 200 / 15.

4. 200 / 15 is approximately equal to 13.33%.

Cross-check

At R = 13.33% for T = 15 years, SI = P x 13.33 x 15 / 100 is approximately 2P, which matches the condition that the interest equals double the principal, confirming the rate.