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

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Senior Manager
Joined: 14 Jul 2006
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This year Henry will save a certain amount of his income, [#permalink]

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23 Aug 2006, 01:51
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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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Director
Joined: 13 Nov 2003
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23 Aug 2006, 04:09
Hallo Apolo,
It=EXt+St
EXn=St*(1+r)

Sn=? if EXn=(EXt/2)
WHERE
t-stands for this year
n-next year
EX -expended
S-saved
I-income
Substitute and get E

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Manager
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23 Aug 2006, 04:23
let us assume he is having x dollars this year,
he spends y dollars, and x-y dollars remains with him
now we hav to calculate (x-y)/x in terms of r
for that we have an equation:
(x-y)(1+r)=y/2
=>x-y=y/[2(1+r)]-----------(eq 1)
x-y+y=y/[2(1+r)]+y=>x=[y(3+2r)]/[2(1+r)]---------(eq 2)
eq 1/eq 2 gives us the answer and its 1/(3+2r)

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Re: This year Henry will save a certain amount of his income, [#permalink]

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14 Oct 2017, 05:21
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Re: This year Henry will save a certain amount of his income,   [#permalink] 14 Oct 2017, 05:21
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