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Joined: 31 Dec 1969
Location: United States
Concentration: Marketing, Other
GMAT 1: 710 Q49 V38
WE: Accounting (Accounting)
Followers: 0
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person will save a certain amnt of income this yr and spend [#permalink]
 08 Sep 2004, 12:07
Question Stats:
0% (00:00) correct
 0% (00:00) wrong based on 0 sessions
person will save a certain amnt of income this yr and spend the rest. next yr person will have no income but for each $ saved this yr, will have 1+r next year. in terms of r wht fraction of the income shud person save so that next year amnt avilable to spend is half the amount spent this year
1. 1/(r+2)
2. 1/(2r+2)
c. 1/(3r+2)
d. 1/(r+3)
e. 1/(2r+3)
please explain
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Manager
Joined: 05 Sep 2004
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Okie dokie.
Let:
I = Total income earned this year
C = Total amount consumed this year
S = Total amount saved this year
i.e., I = C + S
Now, the question imposes the following condition:
Amount available to spend next year = Half the amount spent this year = C/2
Where:
Amount available to spend next year = Amount saved this year * (1+r) = S(1+r)
=> S(1+r) = C/2
=> C = 2S(1+r)
Substituting in our income formula above:
I = 2S(1+r) + S = S[1+2(1+r)] = S(2r+3)
=> S/I = 1/(2r+3) = Portion of I saved this year.
Answer is E.
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Joined: 31 Dec 1969
Location: United States
Concentration: Marketing, Other
GMAT 1: 710 Q49 V38
WE: Accounting (Accounting)
Followers: 0
Kudos [?]:
32
[0], given: 54166
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Perfect Intr3pid. Got the same, used, X (income) and Y (expense for this year = X-$, where $=saving this year) instead. The catch is to read this properly..
For every $ saved this year, the person will have (1+r) next year. Which is $(1+r) = (X-$)/2
=>2$+2r$=X-$
=>3$+2r$=X
=>$(3+2r)=X
Question is X/$=? and we have from above = 1/(3+2r).
E.
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Director
Joined: 16 Jun 2004
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sorry, guest was me...as always forgot to login.
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Director
Joined: 20 Jul 2004
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GMAT Club Legend
Joined: 07 Jul 2004
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Location: Singapore
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Assume person earns $y and save $x, so he spends $y-x
Next year, he wil have $(1+r)x
Amt availble x+rx = y - x
2x+rx = y
x(2+r) = y
x/y = 1/(2+r)
x/y = faction of income that needs to be saved
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