A person borrows money for 4 years at a simple interest rate. If the ratio of the principal to the total interest earned in 4 years is 5 : 1, what is the annual simple interest rate (in % per annum)?

Introduction:
This question tests interpreting a ratio between principal and total interest and converting that ratio into a simple interest rate. Since simple interest is linear, the total interest over a period is a fixed fraction of principal: SI/P = (r*t)/100. Once you identify SI as a fraction of P from the given ratio, the rate follows immediately.

Given Data / Assumptions:

• Principal : total interest in 4 years = 5 : 1
• Time t = 4 years
• Simple interest formula: SI = (P * r * t) / 100
• Therefore SI/P = (r * t) / 100

Concept / Approach:
From the ratio P:SI = 5:1, we get SI = P/5. Substitute into SI = (P*r*4)/100 and cancel P to solve for r. This avoids needing any actual numeric principal value because the ratio already gives the proportional relationship.

Step-by-Step Solution:
Given P : SI = 5 : 1 So SI = P/5 SI = (P * r * 4) / 100 P/5 = (P * r * 4) / 100 Cancel P: 1/5 = (4r) / 100 4r = 20 r = 5

Verification / Alternative check:
At 5% per year for 4 years, SI/P = (5*4)/100 = 20/100 = 1/5, which matches SI = P/5 derived from the ratio. So the rate is consistent.

Why Other Options Are Wrong:
10% would make SI/P = 0.4 in 4 years (ratio 5:2). 20% would make SI/P = 0.8 (ratio 5:4). Higher rates move the ratio away from 5:1.

Common Pitfalls:
Using interest per year instead of total interest for 4 years, or inverting the ratio as SI:P instead of P:SI.

Final Answer:
The annual simple interest rate is 5% per annum.