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A total of 1000$ was invested at compounded annual interest rate. At

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DeeptiM
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A total of 1000$ was invested at compounded annual interest rate. At [#permalink] New post   26 Aug 2011, 23:49
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Well it's a very easy question which I seem to be getting wrong...for most of you this might be like a cherry on the cake hence, would REALLY appreciate if someone can help me with the workings.

A total of 1000$ was invested at compounded annual interest rate. At the end of 12 years, the total value will be 4000$. How many years are needed to reach a total of 8000$.
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Spidy001
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Re: A total of 1000$ was invested at compounded annual interest rate. At [#permalink] New post   27 Aug 2011, 20:14
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Compound Interest A = P(1+r/n)^(nt)

Here n = 1 as its calculated annually.

t = 12

4000 = 1000(1+r)^12

4 = (1+r)^12

=> 4^(1/12) = 1+r equation 1

8000 = 1000(1+r)^n

8 = (1+r)^n

=> 8 = (4^(1/12))^n => 2^3 = 4^(n/12)
=> 2^3 = 2^(n/6)

> 3 = n/6 => n = 18 years
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bodleyev
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Re: A total of 1000$ was invested at compounded annual interest rate. At [#permalink] New post   28 Aug 2011, 16:24
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1000*r^12 = 4000
r^12 = 4
(r^6)^2 = 2^2
r^6 = 2

It takes 6 years for the investment to double.

2 * 2 * 2 = r^6 * r^6 * r^6
8 = r^18

It takes 18 years for the investment to double three times.
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DeeptiM
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Re: A total of 1000$ was invested at compounded annual interest rate. At [#permalink] New post   28 Aug 2011, 21:45
Thanks Spidy & Bodleyev..

+1 to both for helping..
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itznash
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Re: A total of 1000$ was invested at compounded annual interest rate. At [#permalink] New post   29 Aug 2011, 03:34
bodleyev nice way of approcahing the solution .. it definitely saves some time.
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Re: A total of 1000$ was invested at compounded annual interest rate. At [#permalink] New post   19 Feb 2022, 17:03
Hi bodleyev,

I am getting a bit unsure about something with compound interest. Requesting your insights based on the solution you provided.

For any compound interest rate (unknown) if we know that the amount doubles in lets say 9 years, can we say that it will be 4x in 18 years and 8x in 36 years.?

I see the gap is getting larger with the years, meaning the first doubling occured just in a 9 year gap, and the next doubling happened in 18 years. Am I missing some fundamentals here? Thanks
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gmatclubot
Re: A total of 1000$ was invested at compounded annual interest rate. At [#permalink]
19 Feb 2022, 17:03
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