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 \(P\). Then the amount after 25 years is \(5P\).
Simple Interest (SI) \(= \text{Amount} - \text{Principal} = 5P - P = 4P\).
Using the formula for simple interest: \[ SI = \frac{P \times R \times T}{100} \] where \(R\) is the rate of interest and \(T = 25\) years. Substituting: \[ 4P = \frac{P \times R \times 25}{100} \] Dividing both sides by \(P\): \[ 4 = \frac{25R}{100} \implies 4 \times 100 = 25R \implies 400 = 25R \implies R = \frac{400}{25} = 16 \] So, the rate of simple interest is 16% per annum.