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Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

The value of the account today would be \(10,000*1.1*1.05*0.9\). Now, the question is how to calculate this efficiently.

\(10,000*1.1*1.05*0.9=10,000*\frac{11}{10}*\frac{105}{100}*\frac{9}{10}=10,000*\frac{11*105*9}{10,000}\) --> 10,000 will cancel and we'll get: \(11*105*9=(9*11)*105=99*105=(100-1)*105=10,500-105=10,395\).

Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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03 Sep 2012, 06:07

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Value after 1 year: 10,000 * 1.1 = 11,000 Value after 2 years: 11,000 * 1.05 = 11,550 Value today: 11,550 * 0.9 = 10,395

Answer B is correct.

The first equation is easy. In the second, first calculate 10% (1,100) and divide that by 2 (550). Add that to 11,000. In the final equation, calculate 10% again (1,155) and subtract it from 11,550.

Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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03 Sep 2012, 06:51

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Bunuel wrote:

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

This is a question of successive % change. This question ultimately reduces to a multiplication problem. Final value after successive % change on $10,000 = $10,000 X 1.1 X 1.05 X .9 1.1 X 1.05 X .9 = 1.0395 Answer is B)
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Regards SD ----------------------------- Press Kudos if you like my post. Debrief 610-540-580-710(Long Journey): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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03 Sep 2012, 07:45

I also followed the same approach and got the answer as B. But I am wondering if there is any better method of calculating in any problem with successive year interest rates given.
_________________

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

The value of the account today would be \(10,000*1.1*1.05*0.9\). Now, the question is how to calculate this efficiently.

\(10,000*1.1*1.05*0.9=10,000*\frac{11}{10}*\frac{105}{100}*\frac{9}{10}=10,000*\frac{11*105*9}{10,000}\) --> 10,000 will cancel and we'll get: \(11*105*9=(9*11)*105=99*105=(100-1)*105=10,500-105=10,395\).

Answer: B.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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19 Oct 2012, 02:06

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Stupid lucy! If she sees that there is a crisis in the world and her accounts diminishes every year, why hasn't she redraw her money after the second year?!?... I multiplied the last year with 1.1 instead of 0.9 and i got the D answear... This is lucy's fault! :D

Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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15 Dec 2012, 12:14

Bunuel wrote:

SOLUTION

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

The value of the account today would be \(10,000*1.1*1.05*0.9\). Now, the question is how to calculate this efficiently.

\(10,000*1.1*1.05*0.9=10,000*\frac{11}{10}*\frac{105}{100}*\frac{9}{10}=10,000*\frac{11*105*9}{10,000}\) --> 10,000 will cancel and we'll get: \(11*105*9=(9*11)*105=99*105=(100-1)*105=10,500-105=10,395\).

Answer: B.

Thank you for the answer Bunuel, but i was just wondering. When you chose the denominators for the different fractions, was your goal to get 10 000 in the denominator so we could cancel Lucy's initial investment? Smart move by the way

Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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16 Dec 2012, 04:07

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Ans:: the amount at the end of first year will become the principle for 2nd year, applying this trick and calculating we get the amount at the end of third year to be 10395. So the answer is (B).
_________________

Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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02 May 2013, 11:12

.10x10,000= $1,000 end of y1 = 11,000 .05x11,000= $550.00 end of y2 = 11,550 .10x11,550= 1,150 -1,155 (subtract y2 with the loss of y3) end of y3= 10,395

Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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08 Jun 2014, 05:26

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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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10 Sep 2014, 03:43

Bunuel wrote:

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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16 Nov 2014, 08:51

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I cut corners this way: 10% of 10 000=1000 (move the dot one spot) next year you have 11 000 5% of 11 000= 550 (move the dot one spot 1100 = 10%, divide by two to get 5% 1100/2=550) So then you have 11 550, and subtract 10% from this --> 11 550 - 1155. Well it has to be less than 11 000 since more than 1000 is subtracted (eliminating D & E), and it has to end in 5 since you're subtracting a number ending in five (eliminating A & C) that leaves only B.

Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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19 Dec 2015, 09:19

year 1 Increases 10% 1000 Value became 11000 Year 2 increase 5% 550 value became 11550 Year 3 decrease 10% 1155 value became 11550-1155 = $10395.
_________________

Discipline does not mean control. Discipline means having the sense to do exactly what is needed.

Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

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25 May 2016, 09:01

Bunuel wrote:

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

To determine the value of the account today we want to set up an expression showing the various percent increases and decreases.

Remember we are multiplying each percent increase or decrease against the original value of $10,000.

Also, we must remember that a 10% increase is the same as multiplying by 1.1, a 5% increase is the same as multiplying by 1.05, and a 10% decrease is the same as multiplying by 0.9. That is:

10,000(1.1)(1.05)(0.9)

Because the multiplication may get a bit complicated in the equation above, we should convert each decimal to a fraction, allowing us to reduce before multiplying. Thus, we have:

10,000(11/10)(105/100)(9/10)

This is equivalent to: 10,000(11 x 105 x 9/10,000)

Thus we see the the two values of 10,000 cancel out, and we are left with:

11 x 105 x 9 = 99 x 105 = 10,395

Note: If you did not want to perform the multiplication of the final step, you could have used a combination of units digits and estimation to come to the correct answer. Keep in mind that the product of 99 and 105 will have a units digit of 5. That leaves us with only B ($10,395) and E ($12,705) as possible answer choices. Next, by rounding up 99 to 100 and multiplying 100 by 105 we get a product of 10,500. Because we rounded up and answer choice E is LARGER than 10,500, it’s not a possible answer choice. Thus, the correct answer is B, $10,395.
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Jeffrey Miller Scott Woodbury-Stewart Founder and CEO

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Re: Lucy invested $10,000 in a new mutual fund account exactly
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25 May 2016, 09:01

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