Compound Growth Factor Reasoning — From 3× in 3 years to 9× total: If a sum at compound interest becomes 3 times itself in 3 years, in how many years will it become 9 times at the same annual rate?

Introduction / Context:
Compound growth over whole years follows Amount = Principal * (1 + r)^t. If we know the multiplier for a certain time, we can scale to other targets using exponents rather than recomputing rates explicitly.

Given Data / Assumptions:

• (1 + r)^3 = 3 (triples in 3 years)
• Target: (1 + r)^t = 9
• Same annual rate r; find t

Concept / Approach:
Observe that 9 = 3^2. Since (1 + r)^3 = 3, taking powers yields (1 + r)^6 = 3^2 = 9. Therefore, t = 6 years gives the ninefold increase.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 5, 7, 9, 12 years do not align with exponent scaling from a fixed 3-year triple.

Common Pitfalls:

• Using simple interest logic; compounding multiplies factors, not adds linearly.

Final Answer:
6 years.