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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] New post 02 Sep 2012, 19:39
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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, 01:11, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Michelle deposited a certain sum of money in a savings [#permalink] New post 03 Sep 2012, 02:09
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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.

Answer: C.

Similar questions to practice:
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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: Compund Interest [#permalink] New post 02 Sep 2012, 21:59
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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] New post 27 Oct 2013, 21:23
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Michelle deposited a certain sum of money in a savings [#permalink] New post 02 Nov 2013, 02:00
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:
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] New post 02 Nov 2013, 03:42
Expert's post
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:
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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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Michelle deposited a certain sum of money in a savings [#permalink] New post 03 Nov 2013, 00:34
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] New post 10 Jan 2014, 05:41
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] New post 04 Sep 2014, 07:14
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!
Re: Michelle deposited a certain sum of money in a savings   [#permalink] 04 Sep 2014, 07:14
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