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# Interest

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Manager
Joined: 04 Apr 2010
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21 Mar 2011, 20:40
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Question Stats:

50% (02:33) correct 50% (02:41) wrong based on 2 sessions

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An investment with the Brown company yields 10% compounded annually over 2 years, while an investment with Green Corp. yields 20% annually over the same period. If Fernando invests a given amount in Green Corp, by what percent should Rita's initial investment exceed Fernando's, if she wants to invest in Brown but match the final value of his investment?
My answer is 15.7 % but OA is 19%
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Math Forum Moderator
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22 Mar 2011, 02:08
bhandariavi wrote:
An investment with the Brown company yields 10% compounded annually over 2 years, while an investment with Green Corp. yields 20% annually over the same period. If Fernando invests a given amount in Green Corp, by what percent should Rita's initial investment exceed Fernando's, if she wants to invest in Brown but match the final value of his investment?
My answer is 15.7 % but OA is 19%

Let Brown company's investment be b;
After 1 year = 1.1b
After 2 years = 1.1*1.1b = 1.21b

Let Green corp's investment be g;
After 1 year = 1.2g
After 2 years = 1.2g*1.2 = 1.44g

1.21b = 1.44g
b = (1.44/1.21)g = 1.19g(approx)

b should be 19% above g.
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Manager
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22 Mar 2011, 02:12
Let assume that Fernando invests x\$ in Green Corp, while Rita invests y\$ in Brown. Both projects are 2 years long, so finally they will have (this is just a compound interest):

Fernando - x*1.2*1.2=1.44x \$
Rita - y*1.1*1.1=1.21y \$

If their final values are matched (are equal), then 1.44x=1.21y
y=1.44/1.21*x=1.19x

So, Rita should invest by 19% more, than Fernando.
Actually, you probably had some mistake in calculations.

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Manager
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22 Mar 2011, 06:15
But the Green Corp. investment yields annually, right? So the total amt after two yrs form Green Corp. should be,
g+0.2g+0.2g
1.4g
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Manager
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22 Mar 2011, 08:04
bhandariavi wrote:
But the Green Corp. investment yields annually, right? So the total amt after two yrs form Green Corp. should be,
g+0.2g+0.2g
1.4g

hey its compounded annually.
ie if x is the initial amount .....
after 1 year it will be x(1+20/100) =1.2x
after 2 year it will be 1.2x(1+20/100)= 1.2 *1.2 x =1.44x

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Math Forum Moderator
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22 Mar 2011, 08:06
bhandariavi wrote:
But the Green Corp. investment yields annually, right? So the total amt after two yrs form Green Corp. should be,
g+0.2g+0.2g
1.4g

That is the yield if the money gets Simple interest. Here it is compound interest compounded annually.

Compounded annually means that the interest will be applied on the amount available at the end of the year.

Let's say the investment was \$100 compounded annually at 10% rate

After 1 year = 100+100*0.1=100+10=110
After 2 years = 110+110*0.1=110+11=121

With simple interest, the interest is applied at the end of the year on the initial investment

Let's say the investment was \$100 at 10% Simple interest.
After 1 year = 100+100*0.1=100+10=110
After 2 years = 110+100*0.1=110+10=120
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Manager
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22 Mar 2011, 09:10
I know the diff between simple interest and compound interest. But the question doesn't add 'compounded' after 20% so i assume it as simple interest. But the Brown company investment rate compounds annually as the question states.
Thanks to your suggestion - my assumption is wrong.
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22 Mar 2011, 09:19
bhandariavi wrote:
I know the diff between simple interest and compound interest. But the question doesn't add 'compounded' after 20% so i assume it as simple interest. But the Brown company investment rate compounds annually as the question states.
Thanks to your suggestion - my assumption is wrong.

Gotcha!!! Question should be more specific, I agree. In fact, I thought it was a typo and assumed "compounded".
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Re: Interest   [#permalink] 22 Mar 2011, 09:19
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