Posted by **Cyn** on Thursday, December 3, 2009 at 7:45pm.

An amount of money is invested at 12%/a interest. Write an equation and solve it to determine the length of time it will take for the original amouunt to double if the interest is compounded annually.

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**MathMate**, Thursday, December 3, 2009 at 10:33pm
The rule of 72 gives the rough period as 72/12=6 years.

The accurate calculation is as follows:

P=principal

R=interest rate= 1.12 for 12%

n=number of years required.

So

PR^{n}=2P

R^{n}=2

Take log on both sides,

log(R^{n}=log(2)

n*log(R) = log(2)

n=log(2)/log(R)

=log(2)/log(1.12)

=0.3010/0.0492

=6.116 years.

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