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

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This year Henry will save a certian amount of his income and [#permalink]

22 Jul 2006, 05:57

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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22 Jul 2006, 13:35

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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Re: Henry's Savings [#permalink]

22 Jul 2006, 15:35

getzgetzu wrote:

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)

answer = 1/(3+2r)

Re: Henry's Savings [#permalink] 22 Jul 2006, 15:35

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

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

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

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