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

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Senior Manager
Joined: 13 Jun 2005
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Location: Haverhill, MA
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This year Henry will save a certain amount of his income, [#permalink]  16 Jan 2006, 10:32
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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?
Director
Joined: 17 Dec 2005
Posts: 552
Location: Germany
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Kudos [?]: 11 [0], given: 0

Good question!

Will think on it again tomorow.
Senior Manager
Joined: 05 Jan 2005
Posts: 254
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Kudos [?]: 4 [0], given: 0

Reqd rate should be = 100/(3+2r)%

Let Z be the Income and X% the reqd. savings rate.

ZX/100 = Savings in 1st Year
Z(100-X)/100 = Spending in 1st Year

ZX/100(1+r) = Amount available for spending next year

2*ZX/100(1+r)=Z(100-X)/100

2X(1+r) = (100-X)

X(2+ 2R+1 ) = 100

X = 100/(3+2r)
CEO
Joined: 20 Nov 2005
Posts: 2913
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 18

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Re: PS word problem [#permalink]  17 Jan 2006, 15:09
sperumba wrote:
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?

Total income = x
Saved = y
Spent = x-y

Total available to spend next year = y(1+r)

As per question y(1+r) = (x-y)/2

i.e y = x/(3+2r)

Fraction of total income (y/x) = 1/(3+2r)
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

VP
Joined: 20 Sep 2005
Posts: 1023
Followers: 3

Kudos [?]: 27 [0], given: 0

Total income = x(spend) + y(save)

We need to find y/x+y such that

y(r+1) = x/2

y(r+1) = amount available to spend next year
x/2 = half of amount saved this year.

Thus, x = 2y(r+1).

y/( 2y(r+1) + y) = y/y(2r+3) = 1/(2r+3).
Senior Manager
Joined: 05 Jan 2005
Posts: 254
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agree with lhotseface & ps_dahlia for providing ans as fraction. I computed the savings as a %. OA pls ?
Manager
Joined: 04 Jan 2006
Posts: 51
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Let total savings this year = x
Let total spend this year = y
total income = x+y
Next year available income to spend = x(1+r)
Required to find x/x+y

Savings such that x(1+r) = y/2
hence x/y = 1/2(1+r) = 1/2+2r
hence x/x+y = 1/1+2+2r = 1/3+2r
Manager
Joined: 20 Nov 2005
Posts: 188
Location: USA
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Kudos [?]: 2 [0], given: 0

Re: PS word problem [#permalink]  21 Jan 2006, 18:55
sperumba wrote:
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?

you mind, if i ask you where did you get this questions from?
VP
Joined: 21 Sep 2003
Posts: 1066
Location: USA
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Late but got 1/(3+2r) as well. Good question supermba!
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