A sum of money invested at simple interest triples itself in 8 years, meaning that the final amount after 8 years is three times the original principal. At the same rate of simple interest, how many times of the original principal will the amount become in 20 years time?

Introduction / Context:
This question tests conceptual understanding of simple interest and how the amount grows linearly with time. If a sum of money triples in 8 years under simple interest, we can use this information to find the rate of interest and then predict the amount after any other time, such as 20 years. The key property of simple interest is that interest increases in direct proportion to time. This allows us to use ratios or to compute the rate explicitly and apply it to a different time period.

Given Data / Assumptions:

• The sum triples in 8 years under simple interest.
• Final amount after 8 years = 3P, where P is the principal.
• Time for first scenario T1 = 8 years.
• Same rate of simple interest is applied for 20 years in the second scenario.
• We must find the multiple of P that the amount becomes after 20 years.

Concept / Approach:
Under simple interest, the amount after time T is:
A = P * (1 + (R * T) / 100) If the amount after 8 years is 3P, we have:
3P = P * (1 + (R * 8) / 100) Dividing both sides by P, we get:
3 = 1 + (8R / 100) This allows us to find R, the rate of interest per annum. Then, using the same formula for T = 20 years, we can determine how many times the principal the amount becomes by computing 1 + (R * 20) / 100 and interpreting the result as a multiple of P.

Step-by-Step Solution:
From the given condition for 8 years: 3P = P * (1 + 8R / 100). Divide both sides by P: 3 = 1 + 8R / 100. 8R / 100 = 3 − 1 = 2. 8R = 200. R = 200 / 8 = 25% per annum. Now consider 20 years at this rate. Amount after 20 years: A20 = P * (1 + (R * 20) / 100). Substitute R = 25: A20 = P * (1 + (25 * 20) / 100). 25 * 20 = 500, so (R * T) / 100 = 500 / 100 = 5. So A20 = P * (1 + 5) = P * 6. Therefore, after 20 years the amount is 6 times the original principal.

Verification / Alternative check:
We can also reason directly in terms of interest. In 8 years, interest earned is 3P − P = 2P. Thus, in 8 years, simple interest is 2P, so in 1 year, interest is (2P / 8) = P / 4. In 20 years, total interest is (P / 4) * 20 = 5P. Therefore, the amount after 20 years is P + 5P = 6P, which matches the result obtained using the formula approach.

Why Other Options Are Wrong:
8 times, 7 times, 9 times, and 5 times correspond to interest totals of 7P, 6P, 8P, and 4P respectively, which do not align with the rate deduced from the initial 8 year tripling condition. Only 6 times is consistent with the linear accumulation of simple interest at 25% per annum over 20 years.

Common Pitfalls:
Some students confuse simple interest with compound interest and try to raise factors to powers rather than using a linear relationship. Another common error is to misinterpret “triples in 8 years” as meaning the interest is 3P rather than the amount being 3P. Mismanaging ratios or incorrectly solving for R can also lead to wrong results. Focusing on the formula and carefully isolating R first ensures a correct and systematic solution.

Final Answer:
At the same rate of simple interest, the amount will become 6 times the original principal in 20 years.