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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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Updated on: 03 Sep 2012, 02:11
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Difficulty:

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Question Stats:

42% (02:19) correct 58% (02:33) wrong based on 654 sessions

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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%

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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Math Expert
Joined: 02 Sep 2009
Posts: 57022
Re: Michelle deposited a certain sum of money in a savings  [#permalink]

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03 Sep 2012, 03:09
13
34
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.

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Theory:
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Hope it helps.
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Re: Compund Interest  [#permalink]

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02 Sep 2012, 22:59
2
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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Joined: 08 Apr 2012
Posts: 334
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:
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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Posts: 57022
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:
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
1
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.

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.

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
2
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:
john-deposited-10-000-to-open-a-new-savings-account-that-135825.html
http://gmatclub.com/forum/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 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 semi-annually, 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 6-month 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:

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

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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 semi-annually"? Thanks. Else it seems that 8% is the rate for semi-annual compounding.

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

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22 Jul 2018, 06:40
2
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 semi-annually"? Thanks. Else it seems that 8% is the rate for semi-annual 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
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Re: Michelle deposited a certain sum of money in a savings  [#permalink]

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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 semi-annually"? Thanks. Else it seems that 8% is the rate for semi-annual 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.
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Re: Michelle deposited a certain sum of money in a savings  [#permalink]

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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 semi-annually 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 ~ 8.4-1.6=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
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