Which one of the investments below offers the lowest return?Investment A: Invest $1000 for a year and receive $1100. Investment B: Invest $10,000 for 3 months and receive $10,200. Investment C: Invest $500 for half a year and receive $530.

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BlackTom AI · Accepted Answer

Dissecting the problem, we have three investments described with their dollar amounts, time frames, and returns. We will evaluate the return for each over its stated period, and then, if needed, consider annualized returns for comparison.
Option A: Investment A: Invest $1000 for a year and receive $1100. The absolute return over the year is $100 on a $1000 investment, which is a 10% return for that 12-month period. There is no need for annualization here since the time frame given is one year, so the return is 10% for the year.
Option B: Investment B: Invest $10,000 for 3 months and receive $10,200. The absolute return over 3 months is $200 on $10,000, which is a 2% return for the 3-month period. To compare across different time frames, one might annualize this: (1 + 0.02)^4 − 1 ≈ 0.0824, or about 8.24% per year. This shows the 3-month period yields a modest gain, and the annualized figure is roughly 8.2%.
Option C: Investment C: Invest $500 for half a year and receive $530. The absolute return over 6 months is $30 on $500, which is a 6% return for the 6-month period. Annualizing this: (1 + 0.06)^2 − 1 ≈ 0.1236, or about 12.36% per year. This indicates a higher annualized rate than A and B, despite the shorter initial stake.
Now, comparing the three on the basis of the period actually stated (not just annualized): A yields 10% over 12 months, B yields 2% over 3 months, and C yields 6% over 6 months. In terms of the percentage return achieved within each investment’s respective time frame, Investment B’s 2% return over 3 months is the smallest gain among the three. If one were to compare on an annualized basis, B remains the lowest among the three (≈8.24%), while A is 10% and C is ≈12.36% annualized. Misconceptions to watch out for include treating the 2% over 3 months as directly comparable to the 10% over a year without accounting for the differing time horizons, which would misstate which is lowest or highest.
Some common incorrect reasoning would be:
- Assuming the lowest absolute return is always the best benchmark without considering time: here B has the smallest absolute gain (2%), but if you only looked at annualized returns, you still find B to be the lowest among the three in this case.
- Thinking a larger dollar amount invested automatically implies a higher return without considering the rate of return: the $10,000 vs $1000 vs $500 figures affect the dollar amount but not the rate; returns must be evaluated as percentages over their respective periods to compare efficiency.
- Overgeneralizing from one option to others by ignoring compounding and time: for B, compounding over a year lowers the apparent annual yield relative to C, which has a higher annualized rate, illustrating why time framing matters for assessment.
In summary, when focusing on the period-specific percentage gains, Investment B offers the lowest return (2% over 3 months). If one converts to an annualized metric for cross-period comparison, Investment B remains the lowest, at roughly 8.24% per year, while A is 10% and C is about 12.36% annualized.

Which one of the investments below offers the lowest return?Investment A: Invest $1000 for a year and receive $1100. Investment B: Invest $10,000 for 3 months and receive $10,200. Investment C: Invest $500 for half a year and receive $530.

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