Suppose that annual sales for a company were $1,200,000 in 1999.The annual growth rate of sales from 1999 to 2000 was 16 percent,from 2000 to 2001 it was -5 percent,and from 2001 to 2002 it was 22 percent. The geometric mean growth rate of sales over this three-year period is calculated as 10.37 percent.Use the geometric mean growth rate and determine the forecasted sales for 2004.
A)1,780,678
B)1,200,014
C)1,965,337
D)1,613,371
E)1,422,197

Question

Quizplus · Accepted Answer

We can use the geometric mean to find the average annual growth rate over the three-year period:

(1 + 0.16)(1 - 0.05)(1 + 0.22)^(1/3) ≈ 1.1037

This means that, on average, sales grew at a rate of 10.37% per year over the period.

To find the forecasted sales for 2004, we can use the formula:

S = D(1 + r)^n

where S is the forecasted sales in 2004, D is the sales in the last year of the period (2002), r is the growth rate, and n is the number of years into the future (2, since we're finding 2004).

Plugging in the values we know:

D = $1,200,000
r = 0.1037
n = 2

S = $1,200,000(1 + 0.1037)^2 ≈ $1,965,337

Therefore, the forecasted sales for 2004 would be $1,965,337, which is answer choice C.

Suppose That Annual Sales for a Company Were $1,200,000 in 1999.The