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# Last year Luis invested X dollars for one year, half at 8

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Senior Manager
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Last year Luis invested X dollars for one year, half at 8 [#permalink]

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04 Aug 2006, 22:34
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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 invest another X dollars for one year in the same two types of investments, but the lower rate has decreased by 2 percent. If the higher rate is unchanged, what fraction of X dollars must be reinvested at the higher rate so that the total interest earned from the X dollars will be the same for both years?

A. 1/2
B. 3/5
C. 1/3
D. 2/3
E. 4/5
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Director
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05 Aug 2006, 00:25
Lenghty calculations
Total revenue from initial investment is 10% . If 2000 is invested then it is 200\$.
Now X*(6/100)+(2000-X)*(12/100)=200 X=4000/6 should be invested at 6 % and 8000/6 should be invested at 12% to get same revenue. Now (8000/6)/2000=4/6=2/3

Another approach could be (X/2)*8%+(X/2)*12%=X*(6/100)+(2000-X)*(12/100)

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GMAT Instructor
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05 Aug 2006, 00:32
Or ask yourself what weights must be given to 6% and 12% so that the weighted average is 10%. 1:2 will do., so 2/3 must be reinvested at higher rate

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Senior Manager
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05 Aug 2006, 00:35
kevincan wrote:
Or ask yourself what weights must be given to 6% and 12% so that the weighted average is 10%. 1:2 will do., so 2/3 must be reinvested at higher rate

Gr8!.. Thanks Kevin.. It was a nasty calculation..
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Manager
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05 Aug 2006, 13:15
Before change
Interest = x*1*8/200 + x*1*12/200 = 8x/200 + 12x/200 = x/10

After change assume a\$ invested @ 12% amd (x-a) \$ invested @ 6%
x/10 = (x-a)6/100 + 12a/100

simplifying a= 2x/3

Hence D

Heman

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Re: PS:INTEREST   [#permalink] 05 Aug 2006, 13:15
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