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

Question

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

PareshGmat · Accepted Answer

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)

sealberg · Answer

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

Hero8888 · Answer

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

SchruteDwight · Answer

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

ThatDudeKnows · Answer

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.

ThatDudeKnowsPluggingIn

Can,Will · Answer

can somebody explains why R=1 IS 100 % ANNUAL INTEREST ?

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards