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interest ps

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marcodonzelli
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interest ps [#permalink] New post   20 Jan 2008, 22:00
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Lisa invested 1000$ at r% interest compounded semi-annually for one year. Is r greater than 12%?

1. If she had invested the 1000$ at (r+1)% simple interest for one year, she would have received more interest.

2. If she had invested the 1000$ at (r+0.5)% simple interest for one year, she would have received less interest.



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Re: interest ps [#permalink] New post   20 Jan 2008, 22:32
answer is D

Expl : Its a yes/no question . if we assume r=13% , as per first statement
(r+1)/100 > (1+r/100)^2
so we can find out if true or not , in both cases requirement is met

same for second statement

WHATS OFFICIAL ANSWER
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Re: interest ps [#permalink] New post   20 Jan 2008, 23:58
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I misunderstand the conditions:

1. \(\frac{(r+1)}{100} > (1+\frac{r}{100})^2\)

\((\frac{r}{100}+\frac{1}{100})> (1+\frac{2r}{100}+(\frac{r}{100})^2)\)

\(0> (\frac{99}{100}+\frac{r}{100}+(\frac{r}{100})^2)\) is always false.
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Re: interest ps [#permalink] New post   21 Jan 2008, 03:42
walker wrote:
I misunderstand the conditions:

1. \(\frac{(r+1)}{100} > (1+\frac{r}{100})^2\)

\((\frac{r}{100}+\frac{1}{100})> (1+\frac{2r}{100}+(\frac{r}{100})^2)\)

\(0> (\frac{99}{100}+\frac{r}{100}+(\frac{r}{100})^2)\) is always false.



I agree with Walker,
and
2. r^2 + (r+1)^2>0 is always correct.
So B
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Re: interest ps [#permalink] New post   21 Jan 2008, 10:20
marcodonzelli wrote:
Lisa invested 1000$ at r% interest compounded semi-annually for one year. Is r greater than 12%?

1. If she had invested the 1000$ at (r+1)% simple interest for one year, she would have received more interest.

2. If she had invested the 1000$ at (r+0.5)% simple interest for one year, she would have received less interest.


OA is B

1. 1000 (r+1/100)>1000(1+(r/2))^2 - 1000
1000r+10>1000(1+r+r^2/4)-1000=1000r+1000r^2/4
r^2<40/1000====r^2<1/25====r<1/5

2. 1000r+5<1000r+1000r^2/4
r>14% suff
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Re: interest ps [#permalink] New post   23 Jan 2008, 09:14
Hi ! Marco

Now as per the explanation, if 1st statement says r<.2 means condition suff. as answer to the question will be no .



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Re: interest ps [#permalink]
23 Jan 2008, 09:14
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