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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?

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%.

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.

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

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27 Oct 2013, 22:23

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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.

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

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02 Nov 2013, 04:42

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.

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.

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.

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.

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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