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16 Jun 2021, 08:15
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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:
75%
(hard)
Question Stats:
52% (02:17) correct
48%
(02:48)
wrong
based on 193
sessions
History
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Time
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Not Attempted Yet
What is the value of the rate of interest if the difference between the compound interests of the first and the second year is 4 times that of the principal?
(A) 100%
(B) 300%
(C) 100%
(D) 200%
(E) 400%
(A) 100%
(B) 300%
(C) 100%
(D) 200%
(E) 400%
16 Jun 2021, 08:38
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Bunuel
Among other issues, the question is not in English (the phrase "that of" makes no sense in this sentence), two of the answer choices are the same, and it's not clear what it means when it talks about compound interest in the first year, because no compounding has happened at that point. I expect it means to say: if money is invested at r% compounded annually, and the difference in interest earned in the second year and in the first year is 4 times the initial investment, what is the rate of interest?
The size of the initial investment doesn't matter, so we can assume $1 was invested. If we think of the interest rate r as a decimal rather than as a percentage (so we don't need to write "r/100" everywhere), then in the first year, the investment earns $r in interest. The investment is then worth $(1 + r). In the second year, the investment earns $r(1 + r) in interest. The difference in the interest earned in the two years is thus, in dollars,
r(1 + r) - r = r^2
We know this is 4 times the initial investment of $1, so r^2 = 4, and r = 2, or as a percentage, r = 200%.
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cjcalero24
GMAT Focus 2: 635 Q79 V85 DI80 
Posts: 38
23 Aug 2025, 10:25
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Bunuel
I solved this using smart numbers and then checking the answer choices
Assuming the principal is 100, then at the end of year two it should be 400.
From here you do 100(200/100) = 200
Then 200(200/100) = 400
And you see the answer is 200%.
