For simple-interest calculations in engineering economics, if P is principal, i is the interest rate per year, and n is the number of years, what is the interest factor (i.e., the multiplier applied to P to obtain simple interest I)?

Introduction / Context:In many quick appraisals and short-duration loans, simple interest is used to estimate finance charges. Distinguishing between the interest amount I and the accumulated amount F (principal plus interest) is essential. The interest factor refers to the term multiplied by the principal to obtain the interest component under simple interest.

Given Data / Assumptions:

• P: principal (initial investment or loan amount).
• i: annual interest rate (in decimal form).
• n: time in years (number of periods).
• Simple interest convention is used (no compounding).

Concept / Approach:

Under simple interest, the interest I grows linearly with time and rate: I = P * i * n. Therefore, the interest factor is simply i * n. By contrast, the future (accumulated) amount is F = P * (1 + i * n), whose factor for P is (1 + i * n). Clarity between these two avoids common mistakes in quick computations.

Step-by-Step Solution:

Verification / Alternative check:

Worked examples: For P = ₹1000, i = 10% = 0.10, n = 2 years, interest I = 1000 * 0.10 * 2 = ₹200; factor = 0.20 = n * i.

Why Other Options Are Wrong:

• (1 + ni): This is the amount factor for F, not the interest factor.
• (ni − 1) or (1 − ni): Not used in simple-interest basics and can yield negative results for small ni.
• 'None of these': Incorrect because ni is correct.

Common Pitfalls:

• Using compound-interest formulas when the context assumes simple interest.
• Mistaking annual nominal rates for effective rates without clarification.

Final Answer:

ni