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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....

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Intern Joined: 27 Aug 2016 Posts: 1 Re: How much more interest will maria receive if she invests 1000$ for one  [#permalink]

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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
Joined: 01 Jun 2017
Posts: 22

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26 Nov 2018, 06:09
Just take x = 200%
You can solve it in a minute!
Director
Joined: 12 Feb 2015
Posts: 764
Re: How much more interest will maria receive if she invests 1000$for one [#permalink] ### Show Tags 03 Jan 2019, 09:28 email2vm wrote: How much more interest will maria receive if she invests 1000$ 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. _________________ "Please hit +1 Kudos if you like this post" _________________ Manish "Only I can change my life. No one can do it for me" Re: How much more interest will maria receive if she invests 1000$ for one   [#permalink] 03 Jan 2019, 09:28

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