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# person will save a certain amnt of income this yr and spend

Author Message
Joined: 31 Dec 1969
Location: Russian Federation
GMAT 3: 740 Q40 V50
GMAT 4: 700 Q48 V38
GMAT 5: 710 Q45 V41
GMAT 6: 680 Q47 V36
GMAT 9: 740 Q49 V42
GMAT 11: 500 Q47 V33
GMAT 14: 760 Q49 V44
WE: Supply Chain Management (Energy and Utilities)
Followers: 0

Kudos [?]: 233 [0], given: 104586

person will save a certain amnt of income this yr and spend [#permalink]

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08 Sep 2004, 12:07
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person will save a certain amnt of income this yr and spend the rest. next yr person will have no income but for each $saved this yr, will have 1+r next year. in terms of r wht fraction of the income shud person save so that next year amnt avilable to spend is half the amount spent this year 1. 1/(r+2) 2. 1/(2r+2) c. 1/(3r+2) d. 1/(r+3) e. 1/(2r+3) please explain Manager Joined: 05 Sep 2004 Posts: 97 Followers: 1 Kudos [?]: 3 [0], given: 0 ### Show Tags 08 Sep 2004, 13:29 Okie dokie. Let: I = Total income earned this year C = Total amount consumed this year S = Total amount saved this year i.e., I = C + S Now, the question imposes the following condition: Amount available to spend next year = Half the amount spent this year = C/2 Where: Amount available to spend next year = Amount saved this year * (1+r) = S(1+r) => S(1+r) = C/2 => C = 2S(1+r) Substituting in our income formula above: I = 2S(1+r) + S = S[1+2(1+r)] = S(2r+3) => S/I = 1/(2r+3) = Portion of I saved this year. Answer is E. Joined: 31 Dec 1969 Location: Russian Federation Concentration: Entrepreneurship, International Business GMAT 3: 740 Q40 V50 GMAT 4: 700 Q48 V38 GMAT 5: 710 Q45 V41 GMAT 6: 680 Q47 V36 GMAT 9: 740 Q49 V42 GMAT 11: 500 Q47 V33 GMAT 14: 760 Q49 V44 WE: Supply Chain Management (Energy and Utilities) Followers: 0 Kudos [?]: 233 [0], given: 104586 ### Show Tags 08 Sep 2004, 13:47 Perfect Intr3pid. Got the same, used, X (income) and Y (expense for this year = X-$, 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/$=? and we have from above = 1/(3+2r). E. Director Joined: 16 Jun 2004 Posts: 892 Followers: 3 Kudos [?]: 63 [0], given: 0 ### Show Tags 08 Sep 2004, 13:51 sorry, guest was me...as always forgot to login. Director Joined: 20 Jul 2004 Posts: 592 Followers: 2 Kudos [?]: 138 [0], given: 0 ### Show Tags 08 Sep 2004, 19:33 GMAT Club Legend Joined: 07 Jul 2004 Posts: 5045 Location: Singapore Followers: 31 Kudos [?]: 376 [0], given: 0 ### Show Tags 08 Sep 2004, 19:52 Assume person earns$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
08 Sep 2004, 19:52
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