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# Michelle deposited a certain sum of money in a savings

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

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02 Sep 2012, 20:39
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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%
[Reveal] Spoiler: OA

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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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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03 Sep 2012, 03:09
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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.

Similar questions to practice:
john-deposited-10-000-to-open-a-new-savings-account-that-135825.html
on-the-first-of-the-year-james-invested-x-dollars-at-128825.html
marcus-deposited-8-000-to-open-a-new-savings-account-that-128395.html
jolene-entered-an-18-month-investment-contract-that-127308.html
alex-deposited-x-dollars-into-a-new-account-126459.html

Theory:
math-number-theory-percents-91708.html

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

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27 Oct 2013, 22:23
Hello from the GMAT Club BumpBot!

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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.

Similar questions to practice:
john-deposited-10-000-to-open-a-new-savings-account-that-135825.html
on-the-first-of-the-year-james-invested-x-dollars-at-128825.html
marcus-deposited-8-000-to-open-a-new-savings-account-that-128395.html
jolene-entered-an-18-month-investment-contract-that-127308.html
alex-deposited-x-dollars-into-a-new-account-126459.html

Theory:
math-number-theory-percents-91708.html

Hope 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.

Similar questions to practice:
john-deposited-10-000-to-open-a-new-savings-account-that-135825.html
on-the-first-of-the-year-james-invested-x-dollars-at-128825.html
marcus-deposited-8-000-to-open-a-new-savings-account-that-128395.html
jolene-entered-an-18-month-investment-contract-that-127308.html
alex-deposited-x-dollars-into-a-new-account-126459.html

Theory:
math-number-theory-percents-91708.html

Hope 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 semi-annually, 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 semi-annually. 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.

Similar questions to practice:
john-deposited-10-000-to-open-a-new-savings-account-that-135825.html
on-the-first-of-the-year-james-invested-x-dollars-at-128825.html
marcus-deposited-8-000-to-open-a-new-savings-account-that-128395.html
jolene-entered-an-18-month-investment-contract-that-127308.html
alex-deposited-x-dollars-into-a-new-account-126459.html

Theory:
math-number-theory-percents-91708.html

Hope 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
take 100$deposited Balance=100*(1.04)^5=100*1.20(approx)=120. Only C fits C Re: Michelle deposited a certain sum of money in a savings [#permalink] 26 Oct 2015, 00:35 Similar topics Replies Last post Similar Topics: 1 Ann invested a certain sum of money in a bank that paid simple interes 4 14 Mar 2016, 07:55 4 Michele invests some of her money in a mutual fund that 3 22 Mar 2013, 00:59 A certain sum of money is divided among A, B and C such that A gets on 1 17 Oct 2011, 21:13 16 The interest compounded annually on a certain sum of money is$41.60 a 16 23 Apr 2010, 09:29
5 Peter invested a certain sum of money in a simple interest bond whose 10 03 Oct 2009, 04:17
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