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If A is the initial amount put into an account, R is the ann

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mikemcgarry
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If A is the initial amount put into an account, R is the ann [#permalink] New post   22 Jan 2014, 13:32
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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 :-)
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Re: If A is the initial amount put into an account, R is the ann [#permalink] New post   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

= \(A(1 + R)^3 - A\)

= \(A((1 + R)^3 - 1)\)

= \(A((1 + 3R + 3R^2 + R^3 - 1))\)

= \(A(3R + 3R^2 + R^3)\)
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Re: If A is the initial amount put into an account, R is the ann [#permalink] New post   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
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If A is the initial amount put into an account, R is the ann [#permalink] New post   21 Jul 2018, 10:31
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Hi there,

Don't mess with formulas, but pick good numbers. Let's say we have A=$100, R=1 (100% annual interest), so in 1 year we have to get total $100 ours + $100 from interest = $200. Do you see the pattern? $100 (1+1) = $200, so for 3 years Total ammount = $100*(1+1)(1+1)(1+1) = $800, now exclude our own $100, and you will get $700 as profit for 3 years. Check what option will give you $700 with A=$100 and R=1. Only option C does so.

P.S. In case of simple (not compound) interest the formula for interest (only) will look like: $100*1 + $100*1 + $100*1 = $300
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Re: If A is the initial amount put into an account, R is the ann [#permalink] New post   21 Aug 2019, 00:08
A=1000 R=0.1

1st year 1000*0.1 = 100
2nd year (1000+100)*0.1=100+10
3rd year (1000+100+100+10)=100+10+10+1

Total interest
3R+3R^2+R^3
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Re: If A is the initial amount put into an account, R is the ann [#permalink] New post   02 Jul 2022, 15:44
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mikemcgarry wrote:
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 :-)


Variables in the question that are repeated in the answer choices? Let's Plug In!

Picking good numbers can make our lives easy. Let's make A=$1 and R=1 (100%). At the end of the first year, we have $2. At the end of the second year, we have $4. At the end of the third year, we have $8. Interest earned was $8-$1 = $7.

Let's check the answer choices:
(A) \(1(1)^3 = 1\) Nope.
(B) \(1(1 + 1^3) = 2\) Nope.
(C) \(1(3 + 3(1^2) + (1^3)) = 8\) Okayyyyy.
(D) \(3(1)^3 = 3\) Nope.
(E) \(3(1 + 1^2 + 1^3) = 9\) Nope.

Answer choice C.


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Re: If A is the initial amount put into an account, R is the ann [#permalink] New post   28 Nov 2023, 04:28
can somebody explains why R=1 IS 100 % ANNUAL INTEREST ?
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Re: If A is the initial amount put into an account, R is the ann [#permalink]
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