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09 Apr 2016, 04:09
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Difficulty:

65% (hard)

Question Stats:

61% (01:27) correct 39% (01:18) wrong based on 550 sessions

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

[Reveal] Spoiler:
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
[Reveal] Spoiler: OA

Last edited by Nightfury14 on 10 Jan 2017, 10:55, edited 2 times in total.
Hided the OE

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Re: How much more interest will maria receive if she invests 1000$for one [#permalink] ### Show Tags 09 Apr 2016, 04:48 How much more interest will maria receive if she invests 1000$ 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$for one year at x percent annual interest, compounded annually 1000*1.1=1100 Interest amount = 1100-1000=100 Difference in two cases = 210-100 = 110 Putting x=10 in the above option , none of them give 110 as an answer. Could kindly check the options you have posted as it cannot be D as you given the OA. _________________ Kindly press the Kudos to appreciate my post !! Kudos [?]: 57 [0], given: 5 Math Expert Joined: 02 Aug 2009 Posts: 5516 Kudos [?]: 6405 [4], given: 122 Re: How much more interest will maria receive if she invests 1000$ for one [#permalink]

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09 Apr 2016, 04:58
4
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Expert's post
10
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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
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09 Apr 2016, 05:14
5
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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.
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08 May 2016, 22:13
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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
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08 Oct 2016, 23:16
I got this as Q3 on my GMATPrep. Is it possible to receive 700 level questions this early on the GMAT?

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08 Oct 2016, 23:50
1
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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.

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06 Dec 2016, 11:15
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 ?

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10 Apr 2017, 18:02
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.

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Re: How much more interest will maria receive if she invests 1000$for one [#permalink] ### Show Tags 20 Jul 2017, 13:06 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?

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18 Aug 2017, 07:37
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?
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23 Sep 2017, 05:18
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

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