What is the annual rate of interest (per cent per annum)? I. On simple interest, the amount doubles in 5 years. II. For two years, the difference between compound interest and simple interest on this principal is $400. III. The simple interest earned per annum is $2000.

Introduction / Context:
We are to determine the interest rate per annum. In data-sufficiency terms, we must identify which statement(s) alone provide a unique rate without needing actual principal values unless necessary.

Given Data / Assumptions:

• I: On simple interest (SI), the amount doubles in 5 years.
• II: Over 2 years, CI − SI = $400.
• III: SI earned per annum is $2000.

Concept / Approach:
For SI, Amount = Principal * (1 + r * t). If the amount doubles in 5 years, then 1 + r * 5 = 2 ⇒ r = 1/5 = 20% p.a., independent of the principal. Hence Statement I alone directly yields the rate.

Step-by-Step Solution:
From I: doubling on SI in 5 years ⇒ r = 100% / 5 = 20% p.a. Unique and sufficient.From II alone: For 2 years with annual compounding, CI − SI = P * r^2 (since CI over 2y = 2Pr + P r^2; SI over 2y = 2Pr). Without P, r is not determined ⇒ insufficient.From III alone: SI per annum = P * r = 2000; with two unknowns, r is not determined ⇒ insufficient.Note: While II + III together can also yield r (since P r^2 and P r are both known), the minimal sufficiency requested by the options is correctly captured by “Only I”.

Why Other Options Are Wrong:
“Any two” is too broad; many pairs fail. “All three” is overkill when I suffices. “Only II and III” is a sufficient but non-minimal alternative and not the designated answer format here.

Common Pitfalls:
Confusing the requirement to find the rate with the need to know principal; Statement I avoids principal entirely.

Final Answer:
Only Statement I is required (r = 20% p.a.).