GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Oct 2019, 08:28

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

How much more interest will maria receive if she invests 1000$ for one

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15263
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: How much more interest will maria receive if she invests 1000$ for one  [#permalink]

Show Tags

New post 27 Jan 2018, 13:48
Hi All,

This question requires knowledge of the formulas for Simple Interest and Compound Interest:

Simple Interest = Principal x (1 + RT)
Compound Interest = Principal x (1 + R)^T

Where R is the yearly interest rate and T is the number of years. When compounding MORE than once a year, you must divide R by the number of periods and multiply T by the same number of periods.

We're asked for the DIFFERENCE in the amount of interest that is generated under two different situations. We can TEST VALUES to answer this question. IF... X = 20...

$1,000 at 20% compounded semi-annually (meaning twice a year) =

$1,000 x (1.1)^2 =
$1,000 x (1.21) = $1210

$1,000 at 10% compounded annually =

$1,000 x (1.2)^1 =
$1200

The difference is $10, so we're looking for an answer that equals 10 when we plug X=20 into it. There's only one answer that matches....

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Intern
Intern
avatar
B
Joined: 27 Aug 2016
Posts: 1
Re: How much more interest will maria receive if she invests 1000$ for one  [#permalink]

Show Tags

New post 28 Jan 2018, 20:50
[quote="FightToSurvive"]How much more interest will maria receive if she invests 1000$ for one year at x % annual interest, compounded semianually, than if she invest 1000$ for one year at x percent annual interest, compounded annually?

a> 5x
b> 10x
c> x^2/20
d> x^2/40
e>10x+ (x^2/40)

I dont from what source these questions are from.
See from simplification sake, take x =10%
(i) investing 1000$ for one year at x % annual interest, compounded semiannually
1000*1.05*1.05=1102.5
Interest amount = 1102.5-1000=102.5
(ii)investing 1000$ for one year at x percent annual interest, compounded annually
1000*1.1=1100
Interest amount = 1100-1000=100
Difference in two cases = 102.5-100 = 2.5

Putting x=10 in the above option , D gives you the answer
Intern
Intern
avatar
B
Joined: 01 Jun 2017
Posts: 19
How much more interest will maria receive if she invests 1000$ for one  [#permalink]

Show Tags

New post 20 Aug 2018, 07:09
can we use the concept that CI will be slightly larger than SI. hence the difference should also be slightly larger.


in this case, the difference in SI is 0 hence the difference in CI should be slightly larger than 0. Hence x^2/40 is the smallest number out of all and should be the answer.

Bunuel chetan2u
Manager
Manager
User avatar
S
Joined: 28 Jun 2018
Posts: 130
Location: Bouvet Island
GMAT 1: 490 Q39 V18
GMAT 2: 640 Q47 V30
GMAT 3: 670 Q50 V31
GMAT 4: 700 Q49 V36
GPA: 4
Re: How much more interest will maria receive if she invests 1000$ for one  [#permalink]

Show Tags

New post 26 Nov 2018, 06:09
Just take x = 200%
You can solve it in a minute!
Director
Director
User avatar
V
Joined: 12 Feb 2015
Posts: 917
Re: How much more interest will maria receive if she invests 1000$ for one  [#permalink]

Show Tags

New post 03 Jan 2019, 09:28
email2vm wrote:
How much more interest will maria receive if she invests 1000$ for one year at x % annual interest, compounded semianually, than if she invest 1000$ for one year at x percent annual interest, compounded annually?


A. 5x

B. 10x

C. \(\frac{x^2}{20}\)

D. \(\frac{x^2}{40}\)

E. \((10x+\frac{x^2}{40})\)


Here is how i solved only to get it wrong:

let x=100%

annually :

SI = 1000*100/100*1 = 1000
total =1000+1000=2000

semiannually:

Si (for 1st 6 months) = 1000
total after 6 months =2000

Si(for last 6 months) = 2000
total after 6 months= 4000

more interest maria will receive = 2000

====looking for the answer choices

100^2/40 != 2000!!!

where am I wrong? Today it seems I am back to square 1



It is easier to test numbers in this question. Try with x = 20%. One can solve this question in less than 2 minutes.
_________________
________________
Manish :geek:

"Only I can change my life. No one can do it for me"
VP
VP
User avatar
P
Joined: 14 Feb 2017
Posts: 1194
Location: Australia
Concentration: Technology, Strategy
Schools: LBS '22
GMAT 1: 560 Q41 V26
GMAT 2: 550 Q43 V23
GMAT 3: 650 Q47 V33
GMAT 4: 650 Q44 V36
WE: Management Consulting (Consulting)
Reviews Badge CAT Tests
Re: How much more interest will maria receive if she invests 1000$ for one  [#permalink]

Show Tags

New post 10 Jul 2019, 14:48
Got this wrong on an official practice test. Resolving here for retention:

Method 1 - Plug-in values for x (quickest method)

x= 20

Compounded
New balance after compounding is equal to 1000(1+20/200)^2
= 1000(11/10)^2
= 1000(121/100)
= 1210

Simple interest
New balance with interest 1000(1+20/100)^1
= 1000(6/5)
= 1200

'How much more interest' = 1210 - 1200 = 10 more

Plug-in 20 to each answer choice to get 10
A - 5(20) = 200 --> Wrong
B - 10(20) = 200 --> wrong
C - (20)^2/ 20 = 20 --> wrong
D - (20)^2/40 = 10 --> correct
E - (10(2) + (20)^2/40) = 30 --> wrong


Method 2 - Algebraic, but since we have variables, breakdown the compounding periods instead of calculating it all in one go)


Compounding:
1000(1+x/100/2)^1
= 1000 (1 + x/200)^1
= 1000 + 5x
New balance after first compounding period = 1000 + 5x

Second compounding period
Principle *(Interest rate/#compound periods + 1)^compounding period
(1000 + 5x)(1 + x/200)^1
= 1000 + 5x + 5x + (5x^2)/200
= 1000 + 10x + x^2/40
Now we need to eliminate the principle to get the interest portion
= 1000 + 10x + x^2/40 - 1000
= 10x + x^2/40

Simple interest amount
1000(1+ x/100)^1
= 1000 + 10x
Interest portion = 1000+10x - 1000
= 10x

How much more interest?
= 10x + x^2/40 - 10x
= x^2/40
_________________
Goal: Q49, V41

+1 Kudos if I have helped you
GMAT Club Bot
Re: How much more interest will maria receive if she invests 1000$ for one   [#permalink] 10 Jul 2019, 14:48

Go to page   Previous    1   2   [ 26 posts ] 

Display posts from previous: Sort by

How much more interest will maria receive if she invests 1000$ for one

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne