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

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

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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?
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16 Jan 2006, 13:09
Good question!

Will think on it again tomorow.
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16 Jan 2006, 13:14
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)
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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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17 Jan 2006, 15:23
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).
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17 Jan 2006, 17:13
agree with lhotseface & ps_dahlia for providing ans as fraction. I computed the savings as a %. OA pls ?
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19 Jan 2006, 20:06
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
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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?
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21 Jan 2006, 20:41
Late but got 1/(3+2r) as well. Good question supermba!
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21 Jan 2006, 20:41
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