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07 Feb 2026, 07:23
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
59% (02:34) correct
41%
(03:03)
wrong
based on 61
sessions
History
Date
Time
Result
Not Attempted Yet
Laverne invested a certain sum of money at 8% interest compounded quarterly and received 6 months later that sum plus $808 of interest. How much more interest would she have received if she had invested that sum of money for the same m length of time at 12% interest compounded semiannually?
A. $382
B. $392
C. $402
D. $412
E. $422
A. $382
B. $392
C. $402
D. $412
E. $422
poojaarora1818
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07 Feb 2026, 09:07
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Solution:
Given: Rate of Interest = 8%(compounded quarterly)
Time Period = 6 months
Interest = $808
Final Value = P(1 + R/n)^nt=> P(1 + 0.08/4)^4*1/2 = P(1.02)^2
Interest = Final Value - Principle Amount
As we know, 0.0404P = $808 => P = $20000
Now, coming to the next part of the problem
Rate = 12%(compounded semiannually)
F = 20000(1+0.12/2)^2*1/2 =>$21200
Total Interest = Final - Principle amount => 21200-20000=1200.
Difference of first interest amount - second interest amount = 808-1200=$392.
Hence, Option B
Given: Rate of Interest = 8%(compounded quarterly)
Time Period = 6 months
Interest = $808
Final Value = P(1 + R/n)^nt=> P(1 + 0.08/4)^4*1/2 = P(1.02)^2
Interest = Final Value - Principle Amount
As we know, 0.0404P = $808 => P = $20000
Now, coming to the next part of the problem
Rate = 12%(compounded semiannually)
F = 20000(1+0.12/2)^2*1/2 =>$21200
Total Interest = Final - Principle amount => 21200-20000=1200.
Difference of first interest amount - second interest amount = 808-1200=$392.
Hence, Option B
kevincan
08 Feb 2026, 09:27
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Great work poojaarora1818! Your solution is spot-on. Let me add an alternative approach that might help others see the pattern more clearly.
This is a classic **Compound Interest comparison problem**—a favorite GMAT topic that tests whether you understand the mechanics of different compounding frequencies.
**The Key Insight:**
The question is really asking: "What's the DIFFERENCE in interest earned between two scenarios with the same principal and time period but different rates and compounding frequencies?"
**Step 1: Find the principal from the first scenario**
8% quarterly for 6 months means:
- Rate per quarter = 8%/4 = 2%
- Number of quarters = 6 months = 2 quarters
- Multiplier = (1.02)2
Interest earned = $808
So: P × (1.02)2 - P = 808
P × 0.0404 = 808
P = $20,000
**Step 2: Calculate interest in the second scenario**
12% semiannually for 6 months means:
- Rate per half-year = 12%/2 = 6%
- Number of half-years = 6 months = 1 period
- Multiplier = (1.06)1
Interest = 20,000 × 0.06 = $1,200
**Step 3: Find the difference**
$1,200 - $808 = **$392** → Answer B
**Common Trap:** Many students forget that "6 months" means different things for quarterly vs. semiannual compounding. With quarterly, you get 2 full compounding periods. With semiannual, you only get 1. Missing this detail leads to wrong calculations.
**Takeaway:** On compound interest problems with different frequencies, always convert the time period to the NUMBER OF COMPOUNDING PERIODS first—don't just plug numbers into formulas. The GMAT loves testing whether you truly understand what "quarterly" and "semiannually" mean in practice.
This is a classic **Compound Interest comparison problem**—a favorite GMAT topic that tests whether you understand the mechanics of different compounding frequencies.
**The Key Insight:**
The question is really asking: "What's the DIFFERENCE in interest earned between two scenarios with the same principal and time period but different rates and compounding frequencies?"
**Step 1: Find the principal from the first scenario**
8% quarterly for 6 months means:
- Rate per quarter = 8%/4 = 2%
- Number of quarters = 6 months = 2 quarters
- Multiplier = (1.02)2
Interest earned = $808
So: P × (1.02)2 - P = 808
P × 0.0404 = 808
P = $20,000
**Step 2: Calculate interest in the second scenario**
12% semiannually for 6 months means:
- Rate per half-year = 12%/2 = 6%
- Number of half-years = 6 months = 1 period
- Multiplier = (1.06)1
Interest = 20,000 × 0.06 = $1,200
**Step 3: Find the difference**
$1,200 - $808 = **$392** → Answer B
**Common Trap:** Many students forget that "6 months" means different things for quarterly vs. semiannual compounding. With quarterly, you get 2 full compounding periods. With semiannual, you only get 1. Missing this detail leads to wrong calculations.
**Takeaway:** On compound interest problems with different frequencies, always convert the time period to the NUMBER OF COMPOUNDING PERIODS first—don't just plug numbers into formulas. The GMAT loves testing whether you truly understand what "quarterly" and "semiannually" mean in practice.
