Alex deposited x dollars into a new account that earned 8

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Alex deposited x dollars into a new account that earned 8 [#permalink]

23 Jan 2012, 13:12

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Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?

A. w/(1+1.08)
B. w/(1.08+1.16)
C. w/(1.16+1.24)
D. w/(1.08+1.08^2)
E. w/(1.08^2+1.08^2)

I thought as
1.08x+2x(1.08) = w

[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Jan 2012, 18:39, edited 1 time in total.

Edited the answer choices

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Re: Alex deposited x dollars into a new account [#permalink]

23 Jan 2012, 16:37

This post received
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Hi there! I'm happy to contribute to this one!

The question: Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w?

So first, Alex puts in x dollars.

One year goes by, and the x dollar accrues interest ---> x(1.08)

Then, Alex adds another x dollars --> x + x(1.08)

Then the second year goes by, and that whole amount gets multiplied by 1.08 ---> [x + x(1.08)]*(1.08) = x(1.08) + x(1.08)^2 = x[1.08 + (1.08)^2]

We are told this amount, the sum total after two years, equals w, so w = x[1.08 + (1.08)^2]

Dividing by the brackets to solve for x, we get x = w/(1.08 + (1.08)^2)

The answer choices as they appear in your post are technically incorrect, because they are lacking parentheses. If you underestimate the importance of parentheses, they will bite you in the butt over and over again on the real GMAT. Assuming the parentheses were in the right places, the answer would be

[Reveal] Spoiler:

.

The key idea is: the x dollar amount that was in there for both years is multiplied twice by the multiplier. That's why there has to be a factor of (1.08)^2 floating around somewhere.

Does this make sense? Please let me know if you have any questions on what I've said.

Mike

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Re: Alex deposited x dollars into a new account [#permalink]

23 Jan 2012, 18:38

kajolnb wrote:

Account at the end of the first year would be 1.08x dollars. At this time x dollars was deposited, hence the account at the beginning of the second year would be (1.08x+x) dollars. Account at the end of the second year would be (1.08x+x)*1.08=w --> x(1.08^2+1.08)=w --> x=w/(1.08+1.08^2).

Answer: D.
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Re: Alex deposited x dollars into a new account [#permalink] 23 Jan 2012, 18:38

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Alex deposited x dollars into a new account that earned 8

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Alex deposited x dollars into a new account that earned 8

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