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

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Joined: 31 Dec 1969

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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)
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)

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Manager
Joined: 05 Sep 2004
Posts: 97

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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.

Kudos [?]: 5 [0], given: 0

Joined: 31 Dec 1969

Kudos [?]: [0], given:

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)

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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.

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Director
Joined: 16 Jun 2004
Posts: 891

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08 Sep 2004, 13:51
sorry, guest was me...as always forgot to login.

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Director
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08 Sep 2004, 19:33

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GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5034

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Location: Singapore

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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

Kudos [?]: 438 [0], given: 0

08 Sep 2004, 19:52
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# person will save a certain amnt of income this yr and spend

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