A sum of Rs 100 doubles to Rs 200 in 5 years when invested at compound interest, compounded annually. How many additional complete years are required for the same sum to earn another Rs 200 as compound interest, that is, to reach Rs 400 in total?

Introduction / Context:
This question builds on the idea of doubling time under compound interest. We are told that Rs 100 becomes Rs 200 in 5 years, so the amount doubles in that time. We must now determine how many more years it will take for the amount to earn another Rs 200 in interest, reaching Rs 400 in total, under the same compound interest conditions.

Given Data / Assumptions:

• Initial principal P = Rs 100.
• Amount after 5 years A5 = Rs 200.
• Interest is compounded annually at some fixed rate (not explicitly required).
• We need the number of extra years for the amount to increase from Rs 200 to Rs 400.

Concept / Approach:
If a sum doubles in 5 years under a fixed compound interest rate, then every subsequent 5 year period multiplies the amount by 2 again, as long as the rate remains the same. This is because the growth factor over 5 years is 2. Therefore, after another 5 years, the amount will double again, taking Rs 200 to Rs 400.

Step-by-Step Solution:
Initial amount after 5 years: 100 → 200. The growth factor for 5 years is 2 (because 100 * 2 = 200). After another 5 year period at the same rate, the amount will again be multiplied by 2. So 200 will become 200 * 2 = 400. The extra time needed to go from 200 to 400 is therefore another 5 years.

Verification / Alternative Check:
Let the 5 year growth factor be k. We know k = 2 because 100k = 200. After another 5 years, the amount will be 100k^2 = 100 * 4 = 400. So, the total time to reach 400 is 10 years, which is 5 years after it first reached 200.

Why Other Options Are Wrong:
3 years and 6 years are arbitrary and do not match the doubling behaviour controlled by the fixed 5 year doubling period. 7 years is more than needed and would give an amount higher than 400, not exactly another doubling.

Common Pitfalls:
Some learners confuse simple interest and compound interest and assume that another Rs 200 will take the same time proportionally, which is not correct. Others may think the rate changes after 5 years, which is not stated in the question.

Final Answer:
The sum requires 5 more years to earn another Rs 200 and reach Rs 400.