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In Episode 3 of our GMAT Ninja Critical Reasoning series, we tackle Discrepancy, Paradox, and Explain an Oddity questions. You know the feeling: the passage gives you two facts that seem completely contradictory....- May 08
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22 Jan 2014, 13:32
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
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Question Stats:
68% (02:14) correct
32%
(01:52)
wrong
based on 558
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If A is the initial amount put into an account, R is the annual percentage of interest written as a decimal, and the interest compounds annually, then which of the following would be an expression, in terms of A and R, for the interest accrued in three years?
(A) \(A(R)^3\)
(B) \(A(R + R^3)\)
(C) \(A(3R + 3R^2 + R^3)\)
(D) \(3A(R)^3\)
(E) \(3A(R + R^2 + R^3)\)
For a discussion of simple vs. compound interest, as well as a full explanation to this question, see:
https://magoosh.com/gmat/2014/compound-i ... -the-gmat/
Mike
(A) \(A(R)^3\)
(B) \(A(R + R^3)\)
(C) \(A(3R + 3R^2 + R^3)\)
(D) \(3A(R)^3\)
(E) \(3A(R + R^2 + R^3)\)
For a discussion of simple vs. compound interest, as well as a full explanation to this question, see:
https://magoosh.com/gmat/2014/compound-i ... -the-gmat/
Mike
13 Mar 2014, 01:31
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Answer = C
Compound Interest Formula:
\(FA = P (1+\frac{r}{100})^n\)
FA = Final Amount (Including compound interest)
P = Principal
r = rate of interest
n = no of years
Here Principal Amount = A
\(FA = A(1 + R)^3\)
Interest Accured = FA - P
= \(A(1 + R)^3 - A\)
= \(A((1 + R)^3 - 1)\)
= \(A((1 + 3R + 3R^2 + R^3 - 1))\)
= \(A(3R + 3R^2 + R^3)\)
Compound Interest Formula:
\(FA = P (1+\frac{r}{100})^n\)
FA = Final Amount (Including compound interest)
P = Principal
r = rate of interest
n = no of years
Here Principal Amount = A
\(FA = A(1 + R)^3\)
Interest Accured = FA - P
= \(A(1 + R)^3 - A\)
= \(A((1 + R)^3 - 1)\)
= \(A((1 + 3R + 3R^2 + R^3 - 1))\)
= \(A(3R + 3R^2 + R^3)\)
General Discussion
02 May 2017, 14:49
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Proud to say I initially got this question wrong a few months ago on Magoosh, and just got it right in 2 minutes today
Year 1: A(1+R)
Year 2: A(1+R)(1+R) = A(1+2R+R^2) = A+2RA+AR^2
Year 3: (A+2RA+AR^2)(1+R) = A+2RA+R^2A+RA+2R^2A+R^3A
Simplify: A+3RA+3R^2A+R^3A
Factor out an A: A(3R+3R^2+R^3) Answer C
Year 1: A(1+R)
Year 2: A(1+R)(1+R) = A(1+2R+R^2) = A+2RA+AR^2
Year 3: (A+2RA+AR^2)(1+R) = A+2RA+R^2A+RA+2R^2A+R^3A
Simplify: A+3RA+3R^2A+R^3A
Factor out an A: A(3R+3R^2+R^3) Answer C
