math
posted by Cyn on .
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.

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.