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03 Sep 2012, 05:47
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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? (A)$10,350
(B) $10,395 (C)$10,500
(D) $11,500 (E)$12,705

Practice Questions
Question: 31
Page: 156
Difficulty: 600
[Reveal] Spoiler: OA

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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink] ### Show Tags 03 Sep 2012, 05:47 5 This post received KUDOS Expert's post 1 This post was BOOKMARKED 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?

(A) $10,350 (B)$10,395
(C) $10,500 (D)$11,500
(E) $12,705 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. _________________ Intern Joined: 28 Aug 2012 Posts: 46 Location: Austria GMAT 1: 770 Q51 V42 Followers: 3 Kudos [?]: 43 [1] , given: 3 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

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.
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink] ### Show Tags 03 Sep 2012, 06:51 2 This post received KUDOS 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?

(A) $10,350 (B)$10,395
(C) $10,500 (D)$11,500
(E) $12,705 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) _________________ 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 Manager Joined: 12 Mar 2012 Posts: 172 Location: India Concentration: Technology, General Management GMAT Date: 07-23-2012 WE: Programming (Telecommunications) Followers: 0 Kudos [?]: 46 [0], given: 4 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.
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink] ### Show Tags 07 Sep 2012, 03:06 Expert's post 1 This post was BOOKMARKED 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?

(A) $10,350 (B)$10,395
(C) $10,500 (D)$11,500
(E) $12,705 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. _________________ Manager Joined: 20 Nov 2010 Posts: 224 Followers: 4 Kudos [?]: 22 [1] , given: 38 Re: Lucy invested$10,000 in a new mutual fund account exactly [#permalink]

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07 Sep 2012, 21:56
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10000 + 1000 = 11000
11000 + 550 = 11550
11550 * 0.9 = 10395
(B)
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http://gmatclub.com/forum/massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142
http://gmatclub.com/forum/1001-ds-questions-file-106193.html#p832133
http://gmatclub.com/forum/gmat-prep-critical-reasoning-collection-106783.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html
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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? (A)$10,350
(B) $10,395 (C)$10,500
(D) $11,500 (E)$12,705

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: $$11*105*9=(9*11)*105=99*105=(100-1)*105=10,500-105=10,395$$.

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
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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
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06 Aug 2014, 11:49
We can use successive percentage formula : a+b + ab/100

so in the first two years it will increase 10 + 5 + 10*5/100 = 15.5

and in the second and third year it will be : 15.5 - 10 - 15.5*10/100 = 3.95

so finally the investment will increase by 3.95 %
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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? (A)$10,350
(B) $10,395 (C)$10,500
(D) $11,500 (E)$12,705

Practice Questions
Question: 31
Page: 156
Difficulty: 600

10,000*1.1--> 10% increase in the first year.
11000*1.05 --> 5% increase in second year
10% decrease from 11550 --> 10395
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20 Nov 2014, 01:50
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Say initial value = 100 (avoiding 2 extra 00)

1st Yr >> 10% increase = 100 + 10 = 110

2nd Yr >> 5% increase = 110 + 5.5 = 115.5

3rd Yr >> 10% decrease = 115.5 - 11.55 = 103.95

Resultant = 103.95 * 100 = 10395

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

(A) $10,350 (B)$10,395
(C) $10,500 (D)$11,500
(E) $12,705 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. _________________ Jeffrey Miller Scott Woodbury-Stewart Founder and CEO Re: Lucy invested$10,000 in a new mutual fund account exactly   [#permalink] 25 May 2016, 09:01
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