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Last year Luis invested x dollars for one year, half at 8

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Last year Luis invested x dollars for one year, half at 8 [#permalink] New post 18 Apr 2008, 08:58
Last year Luis invested x dollars for one year, half at 8 percent simple annual interest and the other half at 12 percent simple annual interest. Now he wants to reinvest the x dollars for one year in the same two types of investments, but the lower rate has decreased. If the higher rate is unchanged , what fraction of the x dollars must be reinvested at the 12 percent rate so that the total interest earned from the x dollars will be the same for both years?

1) the lower rate is now 6%
2) the total amount of interest earned from the two investments last eyar was $3000
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Re: investment [#permalink] New post 18 Apr 2008, 09:49
A

last year: 8%*0.5x + 12%*0.5x

1) this year: 6%*kx + (1-k)x*12%
equal 2 sides, we can solve for k : sufficient
2) the total amount does not help. we have 2 variables the ratio k and the new interest
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Re: investment [#permalink] New post 18 Apr 2008, 13:54
puma wrote:
Last year Luis invested x dollars for one year, half at 8 percent simple annual interest and the other half at 12 percent simple annual interest. Now he wants to reinvest the x dollars for one year in the same two types of investments, but the lower rate has decreased. If the higher rate is unchanged , what fraction of the x dollars must be reinvested at the 12 percent rate so that the total interest earned from the x dollars will be the same for both years?

1) the lower rate is now 6%
2) the total amount of interest earned from the two investments last eyar was $3000


A.

(1) Set n = fraction of x needed
Original interest earned = 0.12*(x/2) + 0.08*(x/2) = 0.1x
New interest = 0.12*(x/2 + nx) + 0.06*(x/2)
We want to same interest, so
0.1x = 0.12*(x/2 + nx) + 0.06*(x/2) = 0.06x + 0.12nx + 0.03x
0.1 = 0.06 + 0.12n + 0.03
We can find n, SUFFICIENT

(2) Without knowing the decreased rate, you cannot find how much more money you need. INSUFFICIENT
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Re: investment [#permalink] New post 18 Apr 2008, 19:37
puma wrote:
Last year Luis invested x dollars for one year, half at 8 percent simple annual interest and the other half at 12 percent simple annual interest. Now he wants to reinvest the x dollars for one year in the same two types of investments, but the lower rate has decreased. If the higher rate is unchanged , what fraction of the x dollars must be reinvested at the 12 percent rate so that the total interest earned from the x dollars will be the same for both years?

1) the lower rate is now 6%
2) the total amount of interest earned from the two investments last eyar was $3000


A little more information on why #2 is wrong:

Year 1 - 8%(x/2) + 12%(x/2) = $3,000
4%x + 6%x = $3,000
10%x = $3,000
x = $30,000

Year 2 - I%(x) + 12%(1-x) = $3,000

You have two variables I and x to solve for and thus #2 is unsolvable.
Re: investment   [#permalink] 18 Apr 2008, 19:37
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