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# Grace and its deposit

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Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
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Kudos [?]: 150 [0], given: 216

Grace and its deposit [#permalink]  15 Nov 2011, 14:42
00:00

Difficulty:

5% (low)

Question Stats:

57% (01:05) correct 42% (01:31) wrong based on 14 sessions
Grace makes an initial deposit of x dollars into a savings account with a z percent interest rate, compounded annually. On the same day, Georgia makes an initial deposit of y dollars into a savings account with a z percent annual interest rate, compounded quarterly. Assuming that neither Grace nor Georgia makes any other deposits or withdrawals and that x, y, and z are positive numbers no greater than 50, whose savings account will contain more money at the end of exactly one year?
(1) z = 4
(2) 100y = zx

[Reveal] Spoiler: OA

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Kudos [?]: 50 [1] , given: 2

Re: Grace and its deposit [#permalink]  15 Nov 2011, 17:14
1
KUDOS
B.

B is sufficient due to the constraints in the problem. Since no number can be greater than 50 and Z is the same for both.

100y =zx

Basically says that X is larger than Y. The differences between annual and quarterly compounding of an identical interest rate over only one year will be fairly negligible. Assuming Z = 50 which is the most it can equal we are left with 2y = x. So we know that Grace is going to have more money than Georgia at the end of year 1.

Statement 2 is sufficient.

Hope that helps.
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Kudos [?]: 3627 [1] , given: 144

Re: Grace and its deposit [#permalink]  16 Nov 2011, 20:21
1
KUDOS
Expert's post
enigma123 wrote:
Grace makes an initial deposit of x dollars into a savings account with a z percent interest rate, compounded annually. On the same day, Georgia makes an initial deposit of y dollars into a savings account with a z percent annual interest rate, compounded quarterly. Assuming that neither Grace nor Georgia makes any other deposits or withdrawals and that x, y, and z are positive numbers no greater than 50, whose savings account will contain more money at the end of exactly one year?
(1) z = 4
(2) 100y = zx

Responding to a pm:

Actually, u0422811's solution is perfect. That is exactly what went through my mind when I read this question.
Quarterly compounding yields more than annual compounding but the difference is minuscule in % terms.
e.g. if you invest \$10 at 10% annual compounding, you get \$11 at the end of the year.
but if you invest \$10 at 10% quarterly compounding, you get \$11.038 at the end of the year.
You get a small fraction of interest extra.

So x is invested at annual compounding and y at quarterly compounding. If x=y, the amount received from y will be a little more.

Statement 1 tells us z = 4. We need to compare x with y so this is not sufficient.

Statement 2 tells us 100y = zx
x/y = 100/z
Since maximum value of z is 50, x is at least twice of y.
If z% = 50%, amount obtained from x is 1.5x (= 3y) and that obtained from y is a little more than 1.5y.
Definitely an investment of \$x results in a higher amount at the end of the year.

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Re: Grace and its deposit   [#permalink] 16 Nov 2011, 20:21
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