Total compound interest at the end of 3 years — which statements suffice? I. Simple interest (SI) for the same principal, rate, and 3 years is $4,500. II. Rate of interest = 10% per annum (p.c.p.a.). III. Over 3 years, compound interest (CI) exceeds SI by $465.

Introduction / Context:We must determine which statements allow us to compute the total compound interest (CI) after 3 years.

Given Data / Assumptions:

• I: SI over 3 years on the same principal and rate is $4,500.
• II: Annual interest rate r = 10%.
• III: CI − SI over 3 years = $465.

Concept / Approach:Two different sufficient routes exist: (A) Use I + II to find principal, then compute CI directly; (B) Use I + III to add the known excess to SI. Either pair I&II or I&III suffices. Since options do not list a combined alternative, we select one of the sufficient pairs and justify both in the explanation.

Step-by-Step Solution (Route A — I + II):

Alternative Check (Route B — I + III):

Why Other Options Are Wrong:

• Only II and III: Without SI or principal, CI remains unknown.
• Only I or Only II or Only III: Individually insufficient.

Common Pitfalls:Mistaking SI and CI formulas; overlooking that CI − SI for 3 years is independent data that, with SI, gives CI immediately.

Final Answer:Only I and II (Note: Only I and III would also be a sufficient pair.)