A sum of money becomes three times its original value in 8 years at simple interest. What is the rate of interest per annum?

Introduction / Context:
This simple interest question is about understanding how the amount relates to the principal when the sum becomes a multiple of itself over time. When a sum doubles, triples or quadruples at simple interest, we can express the total interest earned as a multiple of the original principal and then find the rate using the standard formula.

Given Data / Assumptions:

• The amount after 8 years is three times the principal
• Time (T) = 8 years
• Interest is calculated at simple interest
• We are asked to find the rate of interest per annum (R)

Concept / Approach:
If a sum becomes three times of itself, the final amount A is 3P, where P is the principal. Simple interest is given by:
SI = A - PSI = 3P - P = 2PNow use the simple interest formula:
SI = (P * R * T) / 100Substitute SI = 2P and T = 8 to find R.

Step-by-Step Solution:
We know SI = 2PUsing the formula: SI = (P * R * T) / 100So 2P = (P * R * 8) / 100Cancel P on both sides: 2 = (R * 8) / 100Multiply both sides by 100: 200 = 8RSo R = 200 / 8 = 25Therefore, the rate of interest is 25% per annum
Verification / Alternative check:
Assume a convenient principal such as Rs. 100. If the rate is 25% per annum for 8 years, the interest is:
SI = (100 * 25 * 8) / 100 = 200Final amount = 100 + 200 = 300This is three times the principal, which confirms that 25% is the correct rate.

Why Other Options Are Wrong:
At 30% for 8 years, the interest would be 240% of the principal, making the amount 3.4 times the principal. At 22% or 18%, the total interest is less than 200% of the principal in 8 years, so the amount would be less than three times the principal. Hence, these options do not satisfy the condition given in the question.

Common Pitfalls:
Sometimes students mistake the factor of three as interest of 3P instead of 2P. Remember that amount equals principal plus interest. If amount is three times the principal, the interest is only twice the principal. Misunderstanding this relationship leads to wrong equations and wrong rates.

Final Answer:
The rate of simple interest per annum is 25%.