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# Lucy invested $10,000 in a new mutual fund account exactly  Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: Math Expert Joined: 02 Sep 2009 Posts: 18856 Followers: 3275 Kudos [?]: 22917 [0], given: 2651 Lucy invested$10,000 in a new mutual fund account exactly [#permalink]  03 Sep 2012, 04:47
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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

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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink] 03 Sep 2012, 04:47 1 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: 48 Location: Austria GMAT 1: 770 Q51 V42 Followers: 3 Kudos [?]: 29 [0], given: 3 Re: Lucy invested$10,000 in a new mutual fund account exactly [#permalink]  03 Sep 2012, 05:07
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] 03 Sep 2012, 05:51 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): from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html Manager Joined: 12 Mar 2012 Posts: 171 Location: India Concentration: Technology, General Management GMAT Date: 07-23-2012 WE: Programming (Telecommunications) Followers: 0 Kudos [?]: 31 [0], given: 4 Re: Lucy invested$10,000 in a new mutual fund account exactly [#permalink]  03 Sep 2012, 06:45
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] 07 Sep 2012, 02:06 Expert's post 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: 227 Followers: 4 Kudos [?]: 6 [1] , given: 38 Re: Lucy invested$10,000 in a new mutual fund account exactly [#permalink]  07 Sep 2012, 20:56
1
KUDOS
10000 + 1000 = 11000
11000 + 550 = 11550
11550 * 0.9 = 10395
(B)
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CR notes
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
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html?hilit=chineseburned

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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink] 19 Oct 2012, 01:06 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 Intern Joined: 06 Jun 2012 Posts: 18 Followers: 0 Kudos [?]: 0 [0], given: 7 Re: Lucy invested$10,000 in a new mutual fund account exactly [#permalink]  15 Dec 2012, 11:14
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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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink] 16 Dec 2012, 03:07 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). _________________ www.mnemoniceducation.com TURN ON YOUR MINDS!!! Manager Joined: 17 Jul 2010 Posts: 126 Followers: 0 Kudos [?]: 23 [0], given: 43 Re: Lucy invested$10,000 in a new mutual fund account exactly [#permalink]  02 May 2013, 10:12
.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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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink] 08 Jun 2014, 04:26 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: Lucy invested$10,000 in a new mutual fund account exactly   [#permalink] 08 Jun 2014, 04:26
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