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Michelle deposited a certain sum of money in a savings [#permalink]
02 Sep 2012, 19:39

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Difficulty:

95% (hard)

Question Stats:

45% (02:35) correct
55% (01:59) wrong based on 224 sessions

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?

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

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]
27 Oct 2013, 21:23

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

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

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

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