SOLUTION: Henry invested $12,000 in a new restaurant. When the restaurant was sold two years later, he received $27,000. Find his average annual return by solving the equation 12,000(1 

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Henry invested $12,000 in a new restaurant. When the restaurant was sold two years later, he received $27,000. Find his average annual return by solving the equation 12,000(1        Log On


   

Question 292600: Henry invested $12,000 in a new
restaurant. When the restaurant was sold two years
later, he received $27,000. Find his average annual
return by solving the equation 12,000(1  r)2 
27,000.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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 * %281%2Bi%29%5E2

Divide both sides of this equation by 12000 to get:

27000%2F12000 = %281%2Bi%29%5E2

Simplify to get:

2.25 = %281%2Bi%29%5E2

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

sqrt%282.25%29 = 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 * %281%2Bi%29%5E2 becomes:

27000 = 12000 * %281.5%29%5E2 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%.