Simple interest on a sum for 5 years is equal to 20% of the principal. In how many years will the simple interest be equal to the principal itself at the same rate of simple interest?

Introduction:
This question tests proportional reasoning in simple interest without needing any actual money values. Under simple interest, SI is directly proportional to time for a fixed principal and fixed rate. If you know that in 5 years the interest equals 20% of principal, you can scale the time to find when interest becomes 100% of principal (i.e., equal to principal). This is a classic time-scaling SI question.

Given Data / Assumptions:

• Time t1 = 5 years
• SI after 5 years = 20% of principal = 0.20P
• Same principal and same rate are used for the new time
• Need t2 such that SI = P (i.e., 100% of principal)
• Simple interest proportionality: SI/P = (r * t) / 100

Concept / Approach:
Since SI is proportional to time under fixed rate and principal, the fraction SI/P increases linearly with time. If SI/P is 0.20 at 5 years, then to reach SI/P = 1.00 (interest equals principal), time must be multiplied by 1.00/0.20 = 5. So t2 = 5 * 5 = 25 years.

Step-by-Step Solution:
Given SI in 5 years = 0.20P We want SI = 1.00P Time scales in the same ratio as interest under simple interest Required scaling factor = 1.00 / 0.20 = 5 t2 = 5 years * 5 = 25 years

Verification / Alternative check:
From SI/P = (r*t)/100: If at 5 years SI/P = 0.20, then (r*5)/100 = 0.20 => r = 4%. For SI=P, we need (4*t)/100 = 1 => t = 25 years. Same result, confirming correctness.

Why Other Options Are Wrong:
20 years would give SI/P = 0.8 (80%), not 100%. 15 and 16 years are even smaller. 30 years would exceed the principal (120%). Only 25 years yields exactly SI = P.

Common Pitfalls:
Mixing up “20% in 5 years” with “20% per year,” or assuming compound growth. Another mistake is adding percentages instead of using proportional scaling.

Final Answer:
The simple interest equals the principal after 25 years.