A sum of money deposited at simple interest doubles itself in 6 years. After a total period of 12 years at the same simple interest rate, the final amount will be how many times the original principal?

Introduction / Context:

This problem is a classic application of simple interest in aptitude tests. It asks you to relate how the amount changes over time when the interest rate is fixed and the growth is linear, not compound.

Given Data / Assumptions:

• The principal amount is P (any positive amount).
• At a constant simple interest rate, the amount doubles in 6 years.
• The same rate is continued for a total duration of 12 years.
• We need to express the final amount after 12 years as a multiple of the principal P.

Concept / Approach:

Under simple interest, the interest each year is constant: Interest = P * R * T / 100, where R is rate per annum and T is time in years. If the amount doubles in 6 years, that tells us how much interest is earned in 6 years. Since simple interest grows linearly with time, in 12 years the interest will be exactly double the 6 year interest.

Step-by-Step Solution:

Verification / Alternative check:

You can assume a convenient value for P, for example P = 100. After 6 years, the amount doubles to 200, so interest is 100 in 6 years. In 12 years, interest will be 200, giving a total of 300, which is 3 times the original 100. This matches our general reasoning.

Why Other Options Are Wrong:

The value 5/2 times and 7/2 times correspond to 2.5P and 3.5P, which do not align with the linear growth over 12 years. Four times the original amount would suggest interest of 3P, which is too high. Two times the original amount corresponds only to 6 years, not 12 years.

Common Pitfalls:

Some learners mistakenly think interest doubles when time doubles regardless of the starting point, leading to confusion with compound interest ideas. Under simple interest, once you know the interest for a given period, you can scale it directly with time.

Final Answer:

After 12 years at the same simple interest rate, the amount will be 3 times the original amount.