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.

Answer 1

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
PRⁿ=2P
Rⁿ=2
Take log on both sides,
log(Rⁿ=log(2)
n*log(R) = log(2)
n=log(2)/log(R)
=log(2)/log(1.12)
=0.3010/0.0492
=6.116 years.