GMAT Changed on April 16th - Read about the latest changes here

 It is currently 24 May 2018, 03:20

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

### Show Tags

Updated on: 28 Jan 2018, 20:55
4
KUDOS
36
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

62% (01:28) correct 38% (01:19) wrong based on 646 sessions

### HideShow timer Statistics

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

100^2/40 != 2000!!!

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

Originally posted by email2vm on 09 Apr 2016, 05:09.
Last edited by Bunuel on 28 Jan 2018, 20:55, edited 3 times in total.
Hided the OE
Current Student
Joined: 18 Sep 2014
Posts: 231
Re: How much more interest will maria receive if she invests 1000$for one [#permalink] ### Show Tags 09 Apr 2016, 05:48 How much more interest will maria receive if she invests 1000$ 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*1.1*1.1=1210
Interest amount = 1210-1000=210
(ii)investing 1000$for one year at x percent annual interest, compounded annually 1000*1.1=1100 Interest amount = 1100-1000=100 Difference in two cases = 210-100 = 110 Putting x=10 in the above option , none of them give 110 as an answer. Could kindly check the options you have posted as it cannot be D as you given the OA. _________________ Kindly press the Kudos to appreciate my post !! Math Expert Joined: 02 Aug 2009 Posts: 5779 Re: How much more interest will maria receive if she invests 1000$ for one [#permalink]

### Show Tags

09 Apr 2016, 05:58
8
KUDOS
Expert's post
8
This post was
BOOKMARKED
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> x^2/20
d> x^2/40
e>10x+ (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

100^2/40 != 2000!!!

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

Ravi

Hi,

the correct way is--

whenever amount is compounded other than annually, reduce the interest that many time and increase the time period that many times..

lets see in this Q..

it is semi annually that is twice in a year...
so our time becomes 2n and rate of interest = r/2..

1) when annually
Amount =$$1000( 1+\frac{r}{100})^1 = 1000(1+\frac{r}{100})$$

2) when semi annually
$$1000( 1+\frac{r}{2*100})^2 = 1000(1+\frac{r}{200}^2)+r/100$$

subtract 1 from 2..
$$1000( 1+\frac{r}{2*100})^2 = 1000(1+\frac{r}{200}^2+\frac{r}{100} - 1000( 1+\frac{r}{100})^1$$..
$$1000(1+\frac{r}{200}^2+\frac{r}{100}-(1+\frac{r}{100})$$..
$$1000(\frac{r}{200}^2)$$ = $$r^2/40$$
D
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

GMAT online Tutor

Manager
Status: folding sleeves up
Joined: 26 Apr 2013
Posts: 149
Location: India
Concentration: Finance, Strategy
GMAT 1: 530 Q39 V23
GMAT 2: 560 Q42 V26
GPA: 3.5
WE: Consulting (Computer Hardware)

### Show Tags

09 Apr 2016, 06:14
6
KUDOS
2
This post was
BOOKMARKED
email2vm wrote:
Gotcha!

But can you please take some value such as 5% or 10% and try to solve it.

And what did I miss in my calculations?

Ravi

My bad, i also missed it.

See Ravi,
if you take x = 10%
Annually,
Its simple 1000*10*1/100=100
Semi annually,
1000(1+10/2*100)^2 = 1102.5
Interest amount = 1102.5-1000 = 102.5

Difference in interest = 102.5-100 = 2.5

Put x = 10 and see option D gives you 2.5. Hence D is the answer.
_________________

Kindly press the Kudos to appreciate my post !!

Current Student
Joined: 18 Sep 2014
Posts: 231

### Show Tags

08 May 2016, 23:13
7
KUDOS
3
This post was
BOOKMARKED
simple soln :

take r = 10%

for annual interest

interest = 1000*10/100 = 100

for semi annual

it will be 5/100 * 1000 = 50 ------> after 6 months interest

after 12 months ========> 5/100 * 1050 + 50 = 52.5 + 50 = 102.5 --------> final interest

SO now gain in interest = 102.5 - 100 = 2.5

A), B) and E) are out since all them contain 10x + ...... (10*10 = 100 + x -----> definitely the increase is not in this range)

test c) x^2/20 = 100/20 = 5 ------> close but wrong

so ans is D) x^2/40

check -----> 100/40 = 10/4 = 5/2 = 2.5 -----> bingo
_________________

You have to dig deep and find out what it takes to reshuffle the cards life dealt you

Senior Manager
Joined: 03 Apr 2013
Posts: 288
Location: India
Concentration: Marketing, Finance
Schools: Simon '20
GMAT 1: 740 Q50 V41
GPA: 3

### Show Tags

09 Oct 2016, 00:16
I got this as Q3 on my GMATPrep. Is it possible to receive 700 level questions this early on the GMAT?
Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3459

### Show Tags

09 Oct 2016, 00:50
1
KUDOS
abhimahna wrote:
Keats wrote:
I got this as Q3 on my GMATPrep. Is it possible to receive 700 level questions this early on the GMAT?

There are two things I wanna say :

1. I don't think this question is of 700 level. It's an easy question. I will count it as 600-650 level. It could be solved in hardly 1 min if you solve with a proper approach.
2. Yes, On GMAT sometimes you may get 700 level questions too early. And if you excel in those, you may head towards your dream score very easily.

1. I see what you have to say abhimahna. I quoted 700 level based on GMATClub stats. Moreover, what might be easy for you (or probably me) might not be easy for the other one.
2. Since I did hit a Q 51 on this GMAT Prep Exam 5 (EP2) with one mistake on Q 30, I genuinely wanted to see if we get high level questions this early (in case of a Q 51). I googled my questions starting Q 2 to Q 7 and except Q 2 (600-700), all were rated as 700 level per GMATClub stats.
Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3459

### Show Tags

06 Dec 2016, 12:15
chetan2u wrote:
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> x^2/20
d> x^2/40
e>10x+ (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

100^2/40 != 2000!!!

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

Ravi

Hi,

the correct way is--

whenever amount is compounded other than annually, reduce the interest that many time and increase the time period that many times..

lets see in this Q..

it is semi annually that is twice in a year...
so our time becomes 2n and rate of interest = r/2..

1) when annually
Amount =$$1000( 1+\frac{r}{100})^1 = 1000(1+\frac{r}{100})$$

2) when semi annually
$$1000( 1+\frac{r}{2*100})^2 = 1000(1+\frac{r}{200}^2)+r/100$$

subtract 1 from 2..
$$1000( 1+\frac{r}{2*100})^2 = 1000(1+\frac{r}{200}^2+\frac{r}{100} - 1000( 1+\frac{r}{100})^1$$..
$$1000(1+\frac{r}{200}^2+\frac{r}{100}-(1+\frac{r}{100})$$..
$$1000(\frac{r}{200}^2)$$ = $$r^2/40$$
D

Hi Chetan,

Could you please tell me how did you deduce the second condition where it says semi annually.. It seems you have seperated r/100. I couldn't figure out how ?
Manager
Joined: 26 Mar 2016
Posts: 77
Location: Greece
GMAT 1: 710 Q51 V34
GPA: 2.9

### Show Tags

10 Apr 2017, 19:02
FightToSurvive 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> 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$for one year at x % annual interest, compounded semiannually 1000*1.1*1.1=1210 Interest amount = 1210-1000=210 (ii)investing 1000$ for one year at x percent annual interest, compounded annually
1000*1.1=1100
Interest amount = 1100-1000=100
Difference in two cases = 210-100 = 110

Putting x=10 in the above option , none of them give 110 as an answer. Could kindly check the options you have posted as it cannot be D as you given the OA.

Your figure for the annual interest is incorrect. Is should be 20%. This gives 200 interest on a principle of 1000 versus interest of 210 when compounded semi-annually. D gives 10.
Intern
Joined: 21 Jun 2016
Posts: 4
Re: How much more interest will maria receive if she invests 1000$for one [#permalink] ### Show Tags 20 Jul 2017, 14:06 I can't quite wrap my head around the semi annual and quarterly compounding interest. I tried the following, but ended up with "A" as my answer: Let X percent be 200 Semi-Annual = 1000(1+200/2*100)^2 == > 1000(2)^2 ==> 4,000 Then interest for semi-annual should equal$3,000

Annual = 1000(1+200/100)^1

Then interest for annual should equal $2,000 Difference in interest is$1,000. Given X = 200, why isn't A correct?
Intern
Joined: 14 Aug 2017
Posts: 13

### Show Tags

18 Aug 2017, 08:37
lpardess wrote:
I have a question about gmat intrests- this question doesnt mention simple intrest or not. should i assume that?
because, lets say 10% intrest annualy- isnt 5% semi annualy as the question implies but 4.88 %. 1000*1.0488=1048.8 for the first half a year and 1048.8*1.048 for the second equels= 1100. which equals to 10%.
so actually on the first 30 seconds I tried to look if there is an answer that says- 0. or after few calculation says it, and look for a sentence that would clear that issue.

so, are we suppose to assume simple intrest?

Hi lpardess,

Welcome to GMATClub :)

First of all, notice that this question contains the word "compounded". So, whenever you see "compounded" word in your question, it has to be compound interest.

If not, take it as simple interest.

Does that make sense?
_________________

My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub
Verbal Resources: All SC Resources at one place | All CR Resources at one place

Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free

Intern
Joined: 14 Aug 2017
Posts: 13

### Show Tags

23 Sep 2017, 06:18
I believe this question can be handled in max 20 sec without getting into much formulas..

If you think about it, the difference is going to be nothing but the interest for last 6 months on the interest of first 6 months..

Interest of first 6 months = ((1000/100)*(x/2)) = 5x

Difference = ((5x/100)*(x/2)) = x^2/40