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Michelle deposited a certain sum of money in a savings [#permalink]
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Updated on: 03 Sep 2012, 02:11
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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%
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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.



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Re: Compund Interest [#permalink]
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02 Sep 2012, 22:59
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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



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Re: Michelle deposited a certain sum of money in a savings [#permalink]
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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.
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Re: Michelle deposited a certain sum of money in a savings [#permalink]
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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%?



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



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Re: Michelle deposited a certain sum of money in a savings [#permalink]
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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!
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Re: Michelle deposited a certain sum of money in a savings [#permalink]
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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!



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



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Re: Michelle deposited a certain sum of money in a savings [#permalink]
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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.



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



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Re: Michelle deposited a certain sum of money in a savings [#permalink]
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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.



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Re: Michelle deposited a certain sum of money in a savings [#permalink]
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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
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