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:

Use the formula \(SI = \frac{P \times R \times T}{100}\) and relate the increase in amount to find the rate.

Answer 1

The Correct Option is B

Let the principal amount be \(P\), rate of interest per annum be \(R\%\), and time \(T = 25\) years.
The amount after 25 years is 5 times the principal, so: \[ A = 5P \] Simple Interest (SI) = Amount - Principal = \[ SI = 5P - P = 4P \] Formula for Simple Interest: \[ SI = \frac{P \times R \times T}{100} \] Substitute values: \[ 4P = \frac{P \times R \times 25}{100} \] \[ 4 = \frac{25R}{100} = \frac{R}{4} \] Multiply both sides by 4: \[ 16 = R \] This calculation gives \(R = 16\%\). But check carefully: Actually, \[ 4P = \frac{P \times R \times 25}{100} \implies 4 = \frac{25R}{100} \implies 4 = \frac{R}{4} \implies R = 16\% \] So the rate is \(16\%\) (correct answer is (a)).