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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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76% (02:05) correct 24% (01:38) wrong based on 121 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] 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
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] 07 Feb 2014, 07:03
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