Compound Interest — Identify rate from “27 times in 3 years”: At what annual compound interest rate will a sum become 27 times itself in 3 years?

Introduction / Context:When a principal multiplies by a known factor over an integer number of years with annual compounding, we can take the matching root of that factor to recover the per-year multiplier. This is a direct application of P(1 + r)^t = final amount.

Given Data / Assumptions:

• Multiplier over 3 years = 27
• Annual compounding
• Find r (per annum)

Concept / Approach:If P becomes 27P in 3 years, then (1 + r)^3 = 27. Take the real cube root: 1 + r = 3. Then subtract 1 to isolate r, and express as a percent.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 100%, 150%, 75%, 50% yield three-year multipliers far less than 27 under compounding.

Common Pitfalls:

• Using simple interest logic; compounding is essential for exponential growth like 27× in 3 years.

Final Answer:200% per annum (compounded annually).