A simple interest earned on a certain principal is three times the principal itself when invested for 16 years. What is the annual rate of simple interest offered?

Introduction / Context:
This problem describes a situation where the simple interest earned is three times the original principal over a certain period. The goal is to determine the annual rate of simple interest that produces this result over 16 years.

Given Data / Assumptions:

• Principal (P) is some positive amount.
• Simple interest (SI) over the full period is three times the principal, so SI = 3P.
• Time (T) = 16 years.
• Rate of simple interest (R%) per annum is unknown.
• Interest is calculated using simple interest, not compound interest.

Concept / Approach:
The simple interest formula is SI = (P * R * T) / 100. Here SI is related directly to P by SI = 3P. Substitute the given relationship into the formula, cancel P from both sides, and solve for R in terms of T and the factor of 3. This yields a direct expression for the rate R%.

Step-by-Step Solution:
Step 1: Write the formula for simple interest: SI = (P * R * T) / 100. Step 2: Given that SI = 3P, substitute into the formula: 3P = (P * R * 16) / 100. Step 3: Cancel P from both sides since P is nonzero: 3 = (R * 16) / 100. Step 4: Rearrange to solve for R: R * 16 = 3 * 100. Step 5: Compute 3 * 100 = 300, so R * 16 = 300. Step 6: R = 300 / 16 = 18.75% per annum.

Verification / Alternative check:
Assume a convenient principal, such as P = 100. At R = 18.75% for T = 16 years, SI = (100 * 18.75 * 16) / 100. This simplifies to 18.75 * 16 = 300. So SI = 300, which is three times the principal (3 * 100). This confirms that 18.75% is correct.

Why Other Options Are Wrong:
13.33%, 14.25%, and 16.98% all lead to a simple interest less than three times the principal over 16 years when substituted into the formula, so they do not satisfy the given condition.

Common Pitfalls:
Some students misinterpret “three times the money” as including the principal itself, confusing SI with amount A. Here, the statement clearly refers to the simple interest being three times the principal. Another mistake is forgetting to cancel P from both sides and incorrectly trying to plug in a specific value for P, which is unnecessary.

Final Answer:
The annual simple interest rate offered is 18.75 %.