Simple interest definition check: For n interest periods, with per-period rate i and principal p, the total simple interest accrued equals which expression?

Introduction / Context:
This question distinguishes simple interest from compound interest. With simple interest, the interest earned each period is calculated only on the original principal, not on accumulated interest. Recognizing the correct formula is essential for quick finance calculations and for setting up more complex cash-flow analyses.

Given Data / Assumptions:

• Principal p is constant over time.
• Per-period simple interest rate i (dimensionless, e.g., 0.08).
• Number of periods n.
• No compounding or reinvestment of interest.

Concept / Approach:
By definition, total simple interest I over n periods is I = p * i * n. The amount (future value) under simple interest would be A = p + I = p * (1 + i * n). In contrast, compound interest uses A = p * (1 + i)^n, which is not a simple-interest relation.

Step-by-Step Solution:
Identify what is asked: total interest I (not future amount).Recall definition: I = p * i * n.Select the corresponding option.

Verification / Alternative check:
Consider p = 100, i = 0.05 per period, n = 3. Simple interest I = 100 * 0.05 * 3 = 15. The future amount would then be 115, matching A = p * (1 + i * n).

Why Other Options Are Wrong:
p (1 + i * n): That is the future amount, not the interest alone.p (1 + i)^n: Compound interest amount (includes interest on interest).p (1 - i * n): Not meaningful for interest accrual.p / (1 + i * n): Resembles present value, not total interest.

Common Pitfalls:
Confusing “interest accrued” with “future amount,” or carelessly substituting the compound interest formula where simple interest is specified.

Final Answer:
p * i * n