Question 292600
F = P * (1+i)^n


F = 27000
P = 12000
i = what you want to find.
n = 2 years


Plug your values into this equation to get:


27000 = 12000 * {{{(1+i)^2}}}


Divide both sides of this equation by 12000 to get:


{{{27000/12000}}} = {{{(1+i)^2}}}


Simplify to get:


2.25 = {{{(1+i)^2}}}


Take the square root of both sides of this equation to get:


{{{sqrt(2.25)}}} = 1+i


Simplify to get:


1.5 = 1+i


Subtract 1 from both aides of the equation to get:


i = .5


That's a 50% growth rate per year.


Plug that value into your original equation to get:


27000 = 12000 * {{{(1+i)^2}}} becomes:


27000 = 12000 * {{{(1.5)^2}}} which becomes:


27000 = 12000 * 2.25 which becomes:


27000 = 27000 confirming that the value of .5 interest rate of growth per year is accurate.


Your answer is that his average annual rate of return is 50%.