Amount investedBalance increaseAccount A$5006% annual interestAccount B$1,000$25 per yearTwo investments were made as shown in the table above. The in...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
| Amount invested | Balance increase | |
|---|---|---|
| Account A | \(\$500\) | \(6\%\) annual interest |
| Account B | \(\$1,000\) | \(\$25\) per year |
Two investments were made as shown in the table above. The interest in Account A is compounded once per year. Which of the following is true about the investments?
Account A always earns more money per year than Account B.
Account A always earns less money per year than Account B.
Account A earns more money per year than Account B at first but eventually earns less money per year.
Account A earns less money per year than Account B at first but eventually earns more money per year.
1. TRANSLATE the problem information
- Given information:
- Account A: $500 principal, 6% annual compound interest
- Account B: $1,000 principal, $25 per year fixed
- The question asks about money EARNED per year, not total balance
2. INFER what we need to compare
- We need to compare annual earnings (interest), not total account values
- Account A's earnings will change each year due to compounding
- Account B's earnings stay constant at $25 per year
3. Calculate first year earnings
Account A: \(\$500 \times 0.06 = \$30\)
Account B: \(\$25\)
Account A earns more in year 1.
4. INFER the long-term pattern
- Account A starts with higher earnings ($30 vs $25)
- Compound interest means Account A's principal grows each year
- Growing principal → growing annual interest
- Account B stays flat at $25 per year
5. Verify with year 2
Account A: New balance = $530, so earnings = \(\$530 \times 0.06 = \$31.80\)
Account B: Still \(\$25\)
The gap widens over time.
Answer: A
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students focus on total account balances instead of annual earnings.
They might calculate that Account B has a higher starting balance ($1,000 vs $500) and conclude that Account B is "better" without actually comparing what each account EARNS per year. This leads to confusion about what the question is actually asking.
This leads to confusion and guessing among the wrong answer choices.
Second Most Common Error:
Inadequate INFER reasoning: Students only compare the first year and don't consider the compounding effect.
They correctly calculate that Account A earns $30 vs Account B's $25 in year 1, but then assume Account A will continue earning exactly $30 each year. They don't realize that compound interest means the earnings grow exponentially, ensuring Account A maintains its advantage permanently.
This may lead them to select Choice C (eventually earns less), thinking the accounts might somehow switch positions over time.
The Bottom Line:
This problem tests whether students understand both what "earnings per year" means and how compound interest creates exponential growth rather than linear growth.
Account A always earns more money per year than Account B.
Account A always earns less money per year than Account B.
Account A earns more money per year than Account B at first but eventually earns less money per year.
Account A earns less money per year than Account B at first but eventually earns more money per year.