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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] New post 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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Re: compounded annually .. spending too much time [#permalink] New post 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.
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Re: compounded annually .. spending too much time [#permalink] New post 04 Nov 2010, 08:41
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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
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Compound Amount [#permalink] New post 13 Feb 2011, 11:52
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Re: Compound Amount [#permalink] New post 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).

Answer: A.
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Re: compounded annually .. spending too much time [#permalink] New post 08 Sep 2012, 20:07
How do you know to divide by 8 and not .08?
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Re: compounded annually .. spending too much time [#permalink] New post 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] New post 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] New post 07 Feb 2014, 07:03
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Re: If money is invested at r percent interest compounded annual [#permalink] New post 17 Feb 2015, 11:43
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Re: If money is invested at r percent interest compounded annual [#permalink] New post 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
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Re: If money is invested at r percent interest compounded annual [#permalink] New post 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.
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Re: If money is invested at r percent interest compounded annual [#permalink] New post 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


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