Aug 18 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes. Aug 19 08:00 AM PDT  09:00 AM PDT Join a 4day FREE online boot camp to kick off your GMAT preparation and get you into your dream bschool in R1.**Limited for the first 99 registrants. Register today! Aug 20 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Aug 20 09:00 PM PDT  10:00 PM PDT Take 20% off the plan of your choice, now through midnight on Tuesday, 8/20 Aug 22 09:00 PM PDT  10:00 PM PDT What you'll gain: Strategies and techniques for approaching featured GMAT topics, and much more. Thursday, August 22nd at 9 PM EDT
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 26 Jul 2010
Posts: 24

Michelle deposited a certain sum of money in a savings
[#permalink]
Show Tags
Updated on: 03 Sep 2012, 02:11
Question Stats:
42% (02:19) correct 58% (02:33) wrong based on 654 sessions
HideShow timer Statistics
Michelle deposited a certain sum of money in a savings account on July 1st, 2007. She earns an 8% interest compounded semiannually. The sum of money in the account on December 31st, 2009 is approximately what percent of the initial deposit? A. 117% B. 120% C. 121% D. 135% E. 140%
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by pgmat on 02 Sep 2012, 20:39.
Last edited by Bunuel on 03 Sep 2012, 02:11, edited 1 time in total.
Renamed the topic and edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 57022

Re: Michelle deposited a certain sum of money in a savings
[#permalink]
Show Tags
03 Sep 2012, 03:09
pgmat wrote: Michelle deposited a certain sum of money in a savings account on July 1st, 2007. She earns an 8% interest compounded semiannually. The sum of money in the account on December 31st, 2009 is approximately what percent of the initial deposit?
A. 117% B. 120% C. 121% D. 135% E. 140% Since Michelle earns 8% interest compounded semiannually, then she earns 4% interest every 6 months. Now, the simple interest earned in 5 periods (30 months = 5*6 months) would be 4%*5=20%. But, since the interest is compounded every 6 months, then there would be interest earned on interest (very small amount) thus the actual interest earned would be a little bit more than 20%, only answer choice C fits. Answer: C. Similar questions to practice: johndeposited10000toopenanewsavingsaccountthat135825.htmlonthefirstoftheyearjamesinvestedxdollarsat128825.htmlmarcusdeposited8000toopenanewsavingsaccountthat128395.htmljoleneenteredan18monthinvestmentcontractthat127308.htmlalexdepositedxdollarsintoanewaccount126459.htmlTheory: mathnumbertheorypercents91708.htmlHope it helps.
_________________




Intern
Joined: 28 Aug 2012
Posts: 40
Location: Austria

Re: Compund Interest
[#permalink]
Show Tags
02 Sep 2012, 22:59
Let's do this roughly:
2.5 years * 8% = 20%
But, there will be some interest on the interest, so the solution will be slightly higher. The next higher solution is 121% and the one thereafter is 135%, which is way too high, the solution must be 121%.
The equation to solve would be: (1 + 0.08/2) ^5



Senior Manager
Joined: 08 Apr 2012
Posts: 334

Re: Michelle deposited a certain sum of money in a savings
[#permalink]
Show Tags
02 Nov 2013, 03:00
Bunuel wrote: pgmat wrote: Michelle deposited a certain sum of money in a savings account on July 1st, 2007. She earns an 8% interest compounded semiannually. The sum of money in the account on December 31st, 2009 is approximately what percent of the initial deposit?
A. 117% B. 120% C. 121% D. 135% E. 140% Since Michelle earns 8% interest compounded semiannually, then she earns 4% interest every 6 months. Now, the simple interest earned in 5 periods (30 months = 5*6 months) would be 4%*5=20%. But, since the interest is compounded every 6 months, then there would be interest earned on interest (very small amount) thus the actual interest earned would be a little bit more than 20%, only answer choice C fits. Answer: C. Similar questions to practice: johndeposited10000toopenanewsavingsaccountthat135825.htmlonthefirstoftheyearjamesinvestedxdollarsat128825.htmlmarcusdeposited8000toopenanewsavingsaccountthat128395.htmljoleneenteredan18monthinvestmentcontractthat127308.htmlalexdepositedxdollarsintoanewaccount126459.htmlTheory: mathnumbertheorypercents91708.htmlHope it helps. But isn't the interest compounded on Jan 1st? Thus making it only 4 periods of interest? and 117%?



Math Expert
Joined: 02 Sep 2009
Posts: 57022

Re: Michelle deposited a certain sum of money in a savings
[#permalink]
Show Tags
02 Nov 2013, 04:42
ronr34 wrote: Bunuel wrote: pgmat wrote: Michelle deposited a certain sum of money in a savings account on July 1st, 2007. She earns an 8% interest compounded semiannually. The sum of money in the account on December 31st, 2009 is approximately what percent of the initial deposit?
A. 117% B. 120% C. 121% D. 135% E. 140% Since Michelle earns 8% interest compounded semiannually, then she earns 4% interest every 6 months. Now, the simple interest earned in 5 periods (30 months = 5*6 months) would be 4%*5=20%. But, since the interest is compounded every 6 months, then there would be interest earned on interest (very small amount) thus the actual interest earned would be a little bit more than 20%, only answer choice C fits. Answer: C. Similar questions to practice: johndeposited10000toopenanewsavingsaccountthat135825.htmlonthefirstoftheyearjamesinvestedxdollarsat128825.htmlmarcusdeposited8000toopenanewsavingsaccountthat128395.htmljoleneenteredan18monthinvestmentcontractthat127308.htmlalexdepositedxdollarsintoanewaccount126459.htmlTheory: mathnumbertheorypercents91708.htmlHope it helps. But isn't the interest compounded on Jan 1st? Thus making it only 4 periods of interest? and 117%? Why do you assume that? On December 31st the whole month is gone, thus interest should be accounted for this month too.
_________________



Senior Manager
Joined: 08 Apr 2012
Posts: 334

Re: Michelle deposited a certain sum of money in a savings
[#permalink]
Show Tags
03 Nov 2013, 01:34
Thanks for the clarification. I am sometimes stumbled by these cases



Manager
Status: Student
Joined: 26 Aug 2013
Posts: 171
Location: France
Concentration: Finance, General Management
GPA: 3.44

Re: Michelle deposited a certain sum of money in a savings
[#permalink]
Show Tags
10 Jan 2014, 06:41
Hi, i get stucked by the 8% here. In theory they should have provide us with the information that the 8% is an annual interest compound semiannually, no? For me She earns an 8% interest compounded semiannually means that the annual interest rate is 16%... Get confused... Nice question!
_________________



Manager
Joined: 23 Sep 2013
Posts: 130
Concentration: Strategy, Marketing
WE: Engineering (Computer Software)

Re: Michelle deposited a certain sum of money in a savings
[#permalink]
Show Tags
04 Sep 2014, 08:14
Paris75,
You are right. This should be 8% annual interest compound semiannually. Then only we can say that it is 4% six monthly. Even I am surprised how they have imagined 8% interest compounded semiannually to be 4%. While it should be 8% which gives an answer as 140%. It must be wrong as per the given language.
Bunuel can please clarify the same?
Thanks!



Intern
Joined: 23 Oct 2012
Posts: 43

Re: Michelle deposited a certain sum of money in a savings
[#permalink]
Show Tags
18 Oct 2014, 01:51
Yes, even i agree with Paris75. Please confirm Bunuel.
_________________



Manager
Status: Applied
Joined: 02 May 2014
Posts: 125
Location: India
Concentration: Operations, General Management
Schools: Tulane '18 (A), Tippie '18 (D), Moore '18, Katz '18 (D), UCSD '18, Madison '18, Olin '18 (S), Simon '18, Desautels '18 (I), Sauder '18 (S), Terry '18 (WL), GWU '18, Neeley '18 (WL), Weatherhead '18 (S), Fox(Temple)'18, Eller FT'18 (A), Schulich Sept"18 (S)
GPA: 3.35
WE: Information Technology (Computer Software)

Re: Michelle deposited a certain sum of money in a savings
[#permalink]
Show Tags
19 Dec 2014, 04:25
Compound interest is always sightly greater than Simple interest. If we consider the above case for simple interest then we have 8 percent simple interest for 2 and 1/2 years so if we consider the amount to be 100 the amount after 2.5 years comes as follows 100*8*2.5/100=20 so amount =120 out of the options A and B are out as they are less and equal respectively options D and E are way larger s option C =121% fits the bill. Hope this one helps.



Manager
Joined: 02 Jul 2015
Posts: 102

Re: Michelle deposited a certain sum of money in a savings
[#permalink]
Show Tags
11 Oct 2015, 22:13
Bunuel wrote: pgmat wrote: Michelle deposited a certain sum of money in a savings account on July 1st, 2007. She earns an 8% interest compounded semiannually. The sum of money in the account on December 31st, 2009 is approximately what percent of the initial deposit?
A. 117% B. 120% C. 121% D. 135% E. 140% Since Michelle earns 8% interest compounded semiannually, then she earns 4% interest every 6 months. Now, the simple interest earned in 5 periods (30 months = 5*6 months) would be 4%*5=20%. But, since the interest is compounded every 6 months, then there would be interest earned on interest (very small amount) thus the actual interest earned would be a little bit more than 20%, only answer choice C fits. Answer: C. Similar questions to practice: johndeposited10000toopenanewsavingsaccountthat135825.htmlonthefirstoftheyearjamesinvestedxdollarsat128825.htmlmarcusdeposited8000toopenanewsavingsaccountthat128395.htmljoleneenteredan18monthinvestmentcontractthat127308.htmlalexdepositedxdollarsintoanewaccount126459.htmlTheory: mathnumbertheorypercents91708.htmlHope it helps. Hi. It seems that the question is missing a vital information. Should it not mention if 8% is the annual interest because as per the existing language it seems to be 8% as interest for 6 months? Please suggest how should it be read for future reference. Till now I have taken it as interest for 6 months instead of an year if the same language is used.



Director
Joined: 23 Jan 2013
Posts: 538

Re: Michelle deposited a certain sum of money in a savings
[#permalink]
Show Tags
26 Oct 2015, 00:35
take 100$ deposited
Balance=100*(1.04)^5=100*1.20(approx)=120. Only C fits
C



Intern
Joined: 05 Jun 2016
Posts: 19

Re: Michelle deposited a certain sum of money in a savings
[#permalink]
Show Tags
08 Nov 2016, 22:04
Bunuel wrote: pgmat wrote: Michelle deposited a certain sum of money in a savings account on July 1st, 2007. She earns an 8% interest compounded semiannually. The sum of money in the account on December 31st, 2009 is approximately what percent of the initial deposit?
A. 117% B. 120% C. 121% D. 135% E. 140% Since Michelle earns 8% interest compounded semiannually, then she earns 4% interest every 6 months. Now, the simple interest earned in 5 periods (30 months = 5*6 months) would be 4%*5=20%. But, since the interest is compounded every 6 months, then there would be interest earned on interest (very small amount) thus the actual interest earned would be a little bit more than 20%, only answer choice C fits. Answer: C. Similar questions to practice: johndeposited10000toopenanewsavingsaccountthat135825.htmlhttp://gmatclub.com/forum/onthefirstoftheyearjamesinvestedxdollarsat128825.htmlmarcusdeposited8000toopenanewsavingsaccountthat128395.htmljoleneenteredan18monthinvestmentcontractthat127308.htmlalexdepositedxdollarsintoanewaccount126459.htmlTheory: mathnumbertheorypercents91708.htmlHope it helps. Hi Brunei , In this question and in the question Highlighted above for the same wording you Consider them differently. If I consider the Highlighted question as correct (as other forum moderator also commented) then why you consider 4 % instead of 16 . please explain.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14785
Location: United States (CA)

Re: Michelle deposited a certain sum of money in a savings
[#permalink]
Show Tags
05 Mar 2018, 12:51
Hi All, This is an interest rate question; based on it's wording, it requires the use of the compound interest formula (although you could calculate the interest every 6 months "by hand"  but that would take a bit of work). In most GMAT questions of this type, interest is calculated once per year, with the following formula: Total = (Principal)(1 + R)^T Principal = the initial money invested R = Interest Rate per year T = Number of years So if you invested $100 at 10% compound interest for 2 years, you'd have…. ($100)(1 + .1)^2 ($100)(1.21) $121 at the end of the two years. In this question, we're calculating interest semiannually, which means we calculate every 6 MONTHS. This changes the calculation a bit. Since we're calculating interest twice a year, we have to essentially "double the T and halve the R." This question includes one more "quirk"  the period of time is NOT in full years  it's five 6month periods. This leads us to…. Principal = $X R = 4% T = 5 periods We can TEST VALUES by picking a number for the Principal: ($100)(1.04)^5 This would be a real tedious calculation IF we didn't have the answers to work with. Since we're receiving 4% interest per period, and there are 5 periods, we know that 4%(5 periods) = 20%…..but since we're compounding the interest, the total would be a little bit more than 20%. There's only one answer here that accounts for the initial Principal and interest that is a little more than 20%. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/



Intern
Status: GMAT in August 2018
Joined: 05 Mar 2018
Posts: 46
Location: India
Concentration: Leadership, Strategy
WE: Law (Consulting)

Re: Michelle deposited a certain sum of money in a savings
[#permalink]
Show Tags
22 Jul 2018, 06:24
Hi chetan2u, Should such a question appear in an actual GMAT exam, would the langauge be tweaked to sth like "8% annual interest, compound semiannually"? Thanks. Else it seems that 8% is the rate for semiannual compounding. Thanks a lot.



Math Expert
Joined: 02 Aug 2009
Posts: 7756

Michelle deposited a certain sum of money in a savings
[#permalink]
Show Tags
22 Jul 2018, 06:40
jayantbakshi wrote: Hi chetan2u, Should such a question appear in an actual GMAT exam, would the langauge be tweaked to sth like "8% annual interest, compound semiannually"? Thanks. Else it seems that 8% is the rate for semiannual compounding. Thanks a lot. yes, almost 100% time it will be worded as you have said.. # 8% annual interest, compounded semiannually # 8% interest per year, compounded semiannually # at a yearly rate of 8%, compounded semiannually if it is ever skipped that also will be rarity.. 8% interest, compounded annually... since it is clear 8% is yearly But most of the times in these cases too it will be mentioned # 8% annual interest, compounded annually
_________________



Intern
Status: GMAT in August 2018
Joined: 05 Mar 2018
Posts: 46
Location: India
Concentration: Leadership, Strategy
WE: Law (Consulting)

Re: Michelle deposited a certain sum of money in a savings
[#permalink]
Show Tags
22 Jul 2018, 07:06
chetan2u wrote: jayantbakshi wrote: Hi chetan2u, Should such a question appear in an actual GMAT exam, would the langauge be tweaked to sth like "8% annual interest, compound semiannually"? Thanks. Else it seems that 8% is the rate for semiannual compounding. Thanks a lot. yes, almost 100% time it will be worded as you have said.. # 8% annual interest year, compounded semiannually # 8% interest per year, compounded semiannually # at a yearly rate of 8%, compounded semiannually if it is ever skipped that also will be rarity.. 8% interest, compounded annually... since it is clear 8% is yearly But most of the times in these cases too it will be mentioned # 8% annual interest year, compounded annually Thanks so much!! You're GREAT!! Cheers.



Senior Manager
Joined: 24 Nov 2016
Posts: 308
Location: United States

Re: Michelle deposited a certain sum of money in a savings
[#permalink]
Show Tags
16 Aug 2019, 10:26
pgmat wrote: Michelle deposited a certain sum of money in a savings account on July 1st, 2007. She earns an 8% interest compounded semiannually. The sum of money in the account on December 31st, 2009 is approximately what percent of the initial deposit?
A. 117% B. 120% C. 121% D. 135% E. 140% 8% compounded semiannually won't be very different from 8% compounded annually; amount=$1000 time=2.5 years first 8% 1000 = 80 second 8% 1000 + 8% 80 = 80 + 6.4 = 86.4 half year 4% 1000 + 4% 167 (~86.4+80) = 40 + 6.8 (5%1% of 167 ~ 8.41.6=6.8.…) interest earned: 80+86.4+46.8 = 166.4+46.8 = 213.2 amount+interest / amount = 1213.2/1000 = ~121% Answer (C).




Re: Michelle deposited a certain sum of money in a savings
[#permalink]
16 Aug 2019, 10:26






