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This year Henry will save a certain amount of his income,

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Senior Manager
Joined: 02 Dec 2007
Posts: 426
This year Henry will save a certain amount of his income, [#permalink]

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20 Sep 2008, 08:50
This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?

A 1/(r+2)
B.1/(2r+2)
C.1/(3r+2)
D.1/(r+3)
E.1/(2r+3)

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Senior Manager
Joined: 02 Dec 2007
Posts: 426

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20 Sep 2008, 09:03
KASSALMD wrote:
Ans is E.

mate can you explain ?
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Joined: 05 Jul 2008
Posts: 1339

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20 Sep 2008, 16:23
Nihit wrote:
KASSALMD wrote:
Ans is E.

mate can you explain ?

Income = I

Savings = S

Spent = (I -S)

so that next year the amount he was available to spend will be equal to half the amount that he spends this year

S(1+r) = 1/2 ( I -S)

S + rS + 1/2 S = 1/2 I

S( 1+ r + 1/2) = 1/2 I

S/I = 1/(2r+3)

Which is what we needed.

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Re: savings   [#permalink] 20 Sep 2008, 16:23
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This year Henry will save a certain amount of his income,

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