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# Jim earns $I this year and will not earn anything next year  Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: Senior Manager Joined: 10 Apr 2012 Posts: 281 Location: United States Concentration: Technology, Other GPA: 2.44 WE: Project Management (Telecommunications) Followers: 3 Kudos [?]: 320 [1] , given: 325 Jim earns$I this year and will not earn anything next year [#permalink]  06 Jul 2013, 08:15
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48% (03:18) correct 52% (02:32) wrong based on 79 sessions
Jim earns $I this year and will not earn anything next year. If he deposits some of his income at First Ranch Savings Bank, he will earn an interest of b per year per dollar deposited. What fraction of his income should Jim deposit, in terms of b, to ensure he spends the same amount next year as he spends this year? (Assume that Jim spends all money that he does not deposit) (A)1/ b+1 (B)1/2b+1 (C)1/3b+2 (D)1/b+2 (E)1/2b+3 [Reveal] Spoiler: OA Math Expert Joined: 02 Sep 2009 Posts: 29186 Followers: 4737 Kudos [?]: 50069 [0], given: 7527 Re: Jim earns$I this year and will not earn anything next year [#permalink]  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 _________________ Manager Joined: 23 May 2013 Posts: 106 Concentration: Strategy, Social Entrepreneurship GMAT Date: 08-05-2015 Followers: 1 Kudos [?]: 50 [1] , given: 29 Re: Jim earns$I this year and will not earn anything next year [#permalink]  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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