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If money is invested at r percent interest compounded annual

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If money is invested at r percent interest compounded annual [#permalink]  04 Nov 2010, 03:53
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Question Stats:

78% (02:05) correct 22% (01:46) wrong based on 183 sessions
If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $5000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of investment 18 years later, when Pat is ready for college? A.$20000
B. $15000 C.$12000
D. $10000 E.$9000
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Sep 2012, 01:48, edited 1 time in total.
Edited the question.
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Re: compounded annually .. spending too much time [#permalink]  04 Nov 2010, 05:21
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vanidhar wrote:
If money is invested at r percent interest, compounded
annually, the amount of the investment will double
in approximately
70/r
years. If Pat’s parents invested
$5,000 in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college? (A)$20,000
(B) $1 5,000 (C)$1 2,000
(D) $1 0,000 (E)$ 9,000

There has to be a logic to why they gave you "If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70/r years."
If r = 8%, the principal will double in 70/8 = apprx 9 years. So in 9 years, 5000 will become 10,000. In another 9 years (i.e. 18 years from now) principal will double again and become $20,000. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Veritas Prep GMAT course is coming to India. Enroll in our weeklong Immersion Course that starts March 29! Veritas Prep Reviews Senior Manager Joined: 20 Jan 2010 Posts: 278 Schools: HBS, Stanford, Haas, Ross, Cornell, LBS, INSEAD, Oxford, IESE/IE Followers: 14 Kudos [?]: 161 [2] , given: 117 Re: compounded annually .. spending too much time [#permalink] 04 Nov 2010, 08:41 2 This post received KUDOS Answer: A Karishma has already explained very well and I would like to add some fact here that would be valuable for our daily life problems. This fact of doubling investment (or growth) after every $$\frac{70}{r}$$ where $$r$$ is the $$%age$$ growth or change per unit time, holds true for real life economy calculations. This isn't just true for this particular question but is actually true for our daily life. Check out the following video link (amazing facts) http://www.youtube.com/watch?v=F-QA2rkpBSY Hope it helps _________________ "Don't be afraid of the space between your dreams and reality. If you can dream it, you can make it so." Target=780 http://challengemba.blogspot.com Kudos?? Senior Manager Joined: 10 Nov 2010 Posts: 268 Location: India Concentration: Strategy, Operations GMAT 1: 520 Q42 V19 GMAT 2: 540 Q44 V21 WE: Information Technology (Computer Software) Followers: 5 Kudos [?]: 88 [0], given: 22 Compound Amount [#permalink] 13 Feb 2011, 11:52 Pls check the image attached Attachments CA.JPG [ 37.48 KiB | Viewed 6197 times ] _________________ The proof of understanding is the ability to explain it. Math Expert Joined: 02 Sep 2009 Posts: 27123 Followers: 4197 Kudos [?]: 40528 [1] , given: 5540 Re: Compound Amount [#permalink] 13 Feb 2011, 12:05 1 This post received KUDOS Expert's post 1 This post was BOOKMARKED If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested$ 5000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of investment 18 years later, when Pat is ready for college?

A. $20000 B.$15000
C. $12000 D.$10000
E. $9000 Since investment doubles in 70/r years then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($5,000*2)*2=$20,000 (after 9 years investment will become$5,000*2=$10,000 and in another 9 years it'll become$10,000*2=$20,000). Answer: A. _________________ Intern Joined: 31 Aug 2012 Posts: 6 Followers: 0 Kudos [?]: 0 [0], given: 0 Re: compounded annually .. spending too much time [#permalink] 08 Sep 2012, 20:07 How do you know to divide by 8 and not .08? Senior Manager Joined: 15 Jun 2010 Posts: 363 Schools: IE'14, ISB'14, Kellogg'15 WE 1: 7 Yrs in Automobile (Commercial Vehicle industry) Followers: 10 Kudos [?]: 202 [0], given: 50 Re: compounded annually .. spending too much time [#permalink] 08 Sep 2012, 22:50 go2013gmat wrote: How do you know to divide by 8 and not .08? Pay attention to the question stem. The relationship is in %age. So no need to divide it by 100. If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70/r years. If Pat’s parents invested$5,000 in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?
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Re: If money is invested at r percent interest compounded annual [#permalink]  09 Sep 2012, 04:44
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Just to brush up a little theory about Simple and Compound Interests calculation.

If P= Principle amount invested
r= annual rate of interest ( For 8% annual rate of interest r=8)
t= time period in years.
Then, $$Simple Interest (SI) = P*r*t$$

For calculation of Compound Interest calculation-
if A=accumulated amount (principle + all interest)
Then, $$A= P*( 1 +$$ $${r/100}$$$$)^t$$
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Re: If money is invested at r percent interest compounded annual [#permalink]  07 Feb 2014, 07:03
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Re: If money is invested at r percent interest compounded annual [#permalink]  17 Feb 2015, 11:43
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Re: If money is invested at r percent interest compounded annual [#permalink]  18 Feb 2015, 01:07
If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $5000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of investment 18 years later, when Pat is ready for college? A.$20000
B. $15000 C.$12000
D. $10000 E.$9000

Amount will get doubled after (70/8) years or 8.75 years
Amount after 8.75 years = 2*5000 = 10000
Amount after 17.5 years = 2*10000 = 20000

Amount after 18 years will be approx to 20000.

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Re: If money is invested at r percent interest compounded annual [#permalink]  03 Mar 2015, 22:12
Hey all,

Just wondering what in the question made you realise you should solve this question via 5,000 x 2 x 2 rather than using the actual interest formula? i.e. P(1+r/n)^nt?

I used the formula then realised the calcs were too complicated.

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Re: If money is invested at r percent interest compounded annual [#permalink]  03 Mar 2015, 22:35
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Hi ColdSushi,

GMAT Quant questions (and the accompanying answer choices) are always carefully written. Sometimes they offer hints as to how you can use estimation to get to the correct answer.

Here, the word 'approximate' in the prompt is essentially telling you to estimate an answer. With an interest rate of 8% and the given formula, you're meant to estimate that the investment will double in 70/8 = about 9 years. The question then asks for the total investment after 18 years. THAT number (18) is not an accident - it was specifically chosen so that you can take advantage of your estimation.

Start = $5000 After 9 years =$10,000
After 18 years = $20,000 Final Answer: [Reveal] Spoiler: A GMAT assassins aren't born, they're made, Rich _________________ Rich Cohen Rich.C@empowergmat.com http://www.empowergmat.com EMPOWERgmat GMAT Club Page, Study Plans, & Discounts http://gmatclub.com/blog/courses/empowergmat-discount/?fl=menu Senior Manager Status: Math is psycho-logical Joined: 07 Apr 2014 Posts: 346 Location: Netherlands GMAT Date: 02-11-2015 WE: Psychology and Counseling (Other) Followers: 0 Kudos [?]: 41 [0], given: 105 Re: If money is invested at r percent interest compounded annual [#permalink] 04 Mar 2015, 03:38 SOURH7WK wrote: go2013gmat wrote: How do you know to divide by 8 and not .08? Pay attention to the question stem. The relationship is in %age. So no need to divide it by 100. If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70/r years. If Pat’s parents invested$5,000 in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?

Also, I guess that even if you did 70 / 0.08 and ended up in 875, this would have alarmed you that it is not possible to wait 875 years for the amount of the investment to doulbe... Even like this, the next thought would be to divide by 8.
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Re: If money is invested at r percent interest compounded annual [#permalink]  04 Mar 2015, 16:30
EMPOWERgmatRichC wrote:
Hi ColdSushi,

GMAT Quant questions (and the accompanying answer choices) are always carefully written. Sometimes they offer hints as to how you can use estimation to get to the correct answer.

Here, the word 'approximate' in the prompt is essentially telling you to estimate an answer. With an interest rate of 8% and the given formula, you're meant to estimate that the investment will double in 70/8 = about 9 years. The question then asks for the total investment after 18 years. THAT number (18) is not an accident - it was specifically chosen so that you can take advantage of your estimation.

Start = $5000 After 9 years =$10,000
After 18 years = $20,000 Rich Ah - ok thank you Rich. I def need to pay more attention to these hints. I find myself 60-70% "there" in solving a question i.e. I'd know what the question is asking and the end point (as opposed to 15-20% "there" when I first started studying for the GMAT) but get stuck because I'd miss an important word or picked a harder way to approach a problem. Hopefully things will get better with practice! Re: If money is invested at r percent interest compounded annual [#permalink] 04 Mar 2015, 16:30 Similar topics Replies Last post Similar Topics: 2 An investment compounds annually at an interest rate of 34.1 5 22 Jun 2013, 21:45 5 If money is invested at r percent interest, compounded annua 10 27 Jan 2013, 22:46 8 If money is invested at r percent interest, compounded annua 6 17 Dec 2012, 05:46 10 The interest compounded annually on a certain sum of money is$41.60 a 15 23 Apr 2010, 08:29
If money is invested at r percent interest, compounded 3 20 Jan 2008, 09:37
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