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Jim earns $I this year and will not earn anything next year

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Jim earns $I this year and will not earn anything next year [#permalink] New post 06 Jul 2013, 08:15
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

42% (02:49) correct 58% (02:29) wrong based on 60 sessions
Jim earns $I this year and will not earn anything next year. If he deposits some of his income at First Ranch Savings Bank, he will earn an interest of b per year per dollar deposited. What fraction of his income should Jim deposit, in terms of b, to ensure he spends the same amount next year as he spends this year? (Assume that Jim spends all money that he does not deposit)
(A)1/ b+1
(B)1/2b+1
(C)1/3b+2
(D)1/b+2
(E)1/2b+3
[Reveal] Spoiler: OA
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Re: Jim earns $I this year and will not earn anything next year [#permalink] New post 06 Jul 2013, 08:22
Expert's post
guerrero25 wrote:
Jim earns $I this year and will not earn anything next year. If he deposits some of his income at First Ranch Savings Bank, he will earn an interest of b per year per dollar deposited. What fraction of his income should Jim deposit, in terms of b, to ensure he spends the same amount next year as he spends this year? (Assume that Jim spends all money that he does not deposit)
(A)1/ b+1
(B)1/2b+1
(C)1/3b+2
(D)1/b+2
(E)1/2b+3


"Stolen" OG question:
Quote:
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. \frac{1}{(r+2)}
B. \frac{1}{2r+2}
C. \frac{1}{3r+2}
D. \frac{1}{r+3}
E. \frac{1}{2r+3}


Discussed here: this-year-henry-will-save-a-certain-amount-of-his-income-100891.html
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Re: Jim earns $I this year and will not earn anything next year [#permalink] New post 25 Feb 2014, 06:55
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For those who want an answer to this question specifically:

This year, Jim ears $1 and deposits x of that into his account, leaving him with (1-x) to spend. Next year, Jim earns an interest of x*b, leaving him with a total of x + x*b in his bank account, also to spend.

Thus, we want to find x such that:

(1 - x) = x + xb
1 = 2x + xb
1 = x(b+2)
x = 1/(b+2)

Answer: D

The key is not to get confused about the interest; don't make the mistake of thinking that he only has x*b to spend, remember that interest is added on to the principle.
Re: Jim earns $I this year and will not earn anything next year   [#permalink] 25 Feb 2014, 06:55
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