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

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guerrero25
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Jim earns $I this year and will not earn anything next year [#permalink] New post   06 Jul 2013, 09:15
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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
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Re: Jim earns $I this year and will not earn anything next year [#permalink] New post   25 Feb 2014, 07:55
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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.
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Re: Jim earns $I this year and will not earn anything next year [#permalink] New post   17 Jun 2022, 16:29
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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


Easiest way to approach problems with variables in both question and answer stem is using numbers plug in numbers
Assume I = 1000, and the amount he deposited in bank as 200, so he has 800 to spend this year and should have 800 next year
Now we need to calculate in terms of pure numbers
To get 800 next year, we need an interest of 600 on our 200 principal so 3 dollars interest for every dollar deposited
so b=3
Fraction deposited = 200/1000 = 1/5 and since b =3, we get 1/b+2 D
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Re: Jim earns $I this year and will not earn anything next year [#permalink] New post   06 Jul 2013, 09:22
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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]
06 Jul 2013, 09:22
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