Compound Interest – Doubling in 5 years: when does it become eight times? If a sum of money placed at compound interest doubles itself in 5 years, in how many years will it become eight times the original principal?

Introduction / Context:
Under compound interest at a constant rate, the time to reach a certain multiple of the principal scales with logarithms of the growth factor. If doubling time is known, other multiples related by powers of 2 can be deduced without computing the exact rate.

Given Data / Assumptions:

• The principal becomes 2P in 5 years
• Same rate and compounding scheme throughout
• Target multiple: 8P

Concept / Approach:
If A = P * (growth_factor)^t and doubling occurs in 5 years, then growth_factor^5 = 2. Eight times means A = 8P = P * (growth_factor)^T. Since 8 = 2^3, we have (growth_factor)^T = (growth_factor)^(3*5) = 2^3. Therefore T = 3 * 5 = 15 years. No explicit rate calculation is required.

Step-by-Step Solution:
Given: time to double = 5 years ⇒ factor^5 = 2Eightfold target: 8 = 2^3Time to reach 8P = 3 × 5 = 15 years

Verification / Alternative check:
Using logs: T = 5 * log(8)/log(2) = 5 * 3 = 15. This confirms the power-of-two reasoning exactly.

Why Other Options Are Wrong:
20, 12, and 10 years correspond to different multiples than 8 given the same doubling time; 25 years is unrelated to a power-of-two multiple based on a 5-year doubling benchmark.

Common Pitfalls:
Confusing simple and compound interest: only compound interest yields constant doubling intervals tied to logarithms. Do not attempt linear interpolation here.

Final Answer:
15 years