Under simple interest, the 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 (in % per annum)?

Introduction:This question tests the relationship between simple interest and principal over time. When interest is expressed as a multiple of the principal, the simple interest formula becomes a clean proportion. Since SI = (P * r * t) / 100 and here SI equals 3P, we can cancel P and solve directly for r. This makes it an easy, direct-recall algebra problem.

Given Data / Assumptions:

• Principal = P
• Time t = 16 years
• Simple interest SI = 3P
• Formula: SI = (P * r * t) / 100

Concept / Approach:Set (P * r * t)/100 = 3P and cancel P from both sides (P is non-zero). Then solve r = (3 * 100) / t. Substitute t = 16 years.

Step-by-Step Solution: SI = (P * r * t) / 100 Given SI = 3P, so (P * r * 16) / 100 = 3P Cancel P: (r * 16) / 100 = 3 r * 16 = 300 r = 300 / 16 = 18.75

Verification / Alternative check:If r = 18.75%, then SI in 16 years is (P * 18.75 * 16)/100 = P * 3, exactly matching “three times the principal.”

Why Other Options Are Wrong:13.33% and 14.25% produce SI less than 3P in 16 years. 16.98% also produces less than 3P. Only 18.75% gives exactly 3P when multiplied by 16 and divided by 100.

Common Pitfalls:Forgetting to cancel P, mixing up “three times the principal” with “principal plus three times,” or using 16 as months instead of years.

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