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 A

Let the principal amount be P, the annual rate of interest be R%, and the time period be T = 25 years.
The final amount after 25 years is 5 times the principal, expressed as:
\[A = 5P\]
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:
\[SI = \frac{P \times R \times T}{100}\]
Substituting the known values:
\[4P = \frac{P \times R \times 25}{100}\]
Simplifying the equation:
\[4 = \frac{25R}{100} = \frac{R}{4}\]
Multiplying both sides by 4 to solve for R:
\[16 = R\]
Therefore, the rate of interest is 16%.