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This year Henry will save a certian amount of his income and

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Joined: 08 Aug 2005
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This year Henry will save a certian amount of his income and [#permalink]  22 Jul 2006, 04:57
This year Henry will save a certian 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 available to spend is equal to half the amount that he spends this year?
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Joined: 20 Nov 2005
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Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
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Let
t - Total income this year
x - amount saved this year
y = amount spent this year
so
t = x + y

Amount available to spend next year = x (1+r) = half of what is spent this year = y/2

so y = 2x(1+r)

t = x + 2x+ 2xr
x/t = 1/(3+2r)
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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Re: Henry's Savings [#permalink]  22 Jul 2006, 14:35
getzgetzu wrote:
This year Henry will save a certian 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 available to spend is equal to half the amount that he spends this year?

This year: spend = income - saving
Next year: money to spend = saving(1+r)

0.5 (income - saving) = saving(1+r)
=> i-s=2s(1+r)
i = s[2(1+r)+1]
i=s[2+2r+1]

s/i=1/(3+2r)

Re: Henry's Savings   [#permalink] 22 Jul 2006, 14:35
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This year Henry will save a certian amount of his income and

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