Question

An amount becomes 5 times its original value in 25 years. What is the rate of simple interest per annum?

• A. 16%
• B. 12%
• C. 20%
• D. 14%

Hint:

For simple interest, use \(SI = \frac{P \times R \times T}{100}\) and relate amount and principal accordingly.

Answer 1

The Correct Option is A

Let the principal amount be denoted by \(P\). After 25 years, the total amount becomes \(5P\).
The simple interest (SI) is calculated as the difference between the final amount and the principal: \(SI = 5P - P = 4P\).
The formula for simple interest is given by: \[SI = \frac{P \times R \times T}{100}\]Here, \(R\) represents the rate of interest, and \(T\) is the time period, which is 25 years. Substituting the known values: \[4P = \frac{P \times R \times 25}{100}\]To find \(R\), we first divide both sides of the equation by \(P\): \[4 = \frac{25R}{100} \implies 4 \times 100 = 25R \implies 400 = 25R \implies R = \frac{400}{25} = 16\]Therefore, the annual rate of simple interest is 16% per annum.