If money is invested at r percent interest compounded annual : GMAT Problem Solving (PS)
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# If money is invested at r percent interest compounded annual

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04 Nov 2010, 03:53
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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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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 Get started with Veritas Prep GMAT On Demand for$199

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Re: compounded annually .. spending too much time [#permalink]

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04 Nov 2010, 08:41
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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)
Hope it helps
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13 Feb 2011, 12:05
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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).

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Re: If money is invested at r percent interest compounded annual [#permalink]

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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 Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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13 Feb 2011, 11:52
Pls check the image attached
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Re: compounded annually .. spending too much time [#permalink]

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08 Sep 2012, 20:07
How do you know to divide by 8 and not .08?
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08 Sep 2012, 22:50
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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? _________________ 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: 24 Jul 2011 Posts: 76 Location: India Concentration: Strategy, General Management GMAT 1: 670 Q49 V33 WE: Asset Management (Manufacturing) Followers: 3 Kudos [?]: 129 [0], given: 5 Re: If money is invested at r percent interest compounded annual [#permalink] ### Show Tags 09 Sep 2012, 04:44 2 This post was BOOKMARKED 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, $$A= P*( 1 +$$ $${r/100}$$$$)^t$$ _________________ My mantra for cracking GMAT: Everyone has inborn talent, however those who complement it with hard work we call them 'talented'. +1 Kudos = Thank You Dear Are you saying thank you? GMAT Club Legend Joined: 09 Sep 2013 Posts: 13459 Followers: 575 Kudos [?]: 163 [0], given: 0 Re: If money is invested at r percent interest compounded annual [#permalink] ### Show Tags 07 Feb 2014, 07:03 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. _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 13459 Followers: 575 Kudos [?]: 163 [0], given: 0 Re: If money is invested at r percent interest compounded annual [#permalink] ### Show Tags 17 Feb 2015, 11:43 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. _________________ Intern Joined: 15 Jan 2015 Posts: 25 Followers: 0 Kudos [?]: 10 [0], given: 1 Re: If money is invested at r percent interest compounded annual [#permalink] ### Show Tags 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. Answer A Intern Joined: 29 Oct 2014 Posts: 25 Followers: 0 Kudos [?]: 9 [0], given: 14 Re: If money is invested at r percent interest compounded annual [#permalink] ### Show Tags 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. Thanks in advance for your help. Senior Manager Status: Math is psycho-logical Joined: 07 Apr 2014 Posts: 443 Location: Netherlands GMAT Date: 02-11-2015 WE: Psychology and Counseling (Other) Followers: 2 Kudos [?]: 109 [0], given: 169 Re: If money is invested at r percent interest compounded annual [#permalink] ### Show Tags 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]

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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! Senior Manager Joined: 23 Sep 2015 Posts: 390 Location: France GMAT 1: 690 Q47 V38 GMAT 2: 700 Q48 V38 WE: Real Estate (Mutual Funds and Brokerage) Followers: 3 Kudos [?]: 60 [0], given: 70 Re: If money is invested at r percent interest compounded annual [#permalink] ### Show Tags 23 Nov 2015, 13:00 ColdSushi wrote: 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. Thanks in advance for your help. Maybe because they said approximate and that they gave 70/r to help. Otherwise, goodluck computing a power of 18 without a calculator _________________ New Application Tracker : update your school profiles instantly! GMAT Club Legend Joined: 09 Sep 2013 Posts: 13459 Followers: 575 Kudos [?]: 163 [0], given: 0 Re: If money is invested at r percent interest compounded annual [#permalink] ### Show Tags 14 Jan 2017, 21:13 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: If money is invested at r percent interest compounded annual [#permalink] 14 Jan 2017, 21:13 Similar topics Replies Last post Similar Topics: 1 How much money must be invested at 10% annual interest, compounded sem 1 17 Jan 2017, 09:04 If John invested$ 1 at 5 percent interest compounded annually, the to 2 27 Dec 2015, 08:42
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