(a) Estimate the value of the ENR construction cost index by using the average (compounded) percentage change in its value between 1995 and 2005 to predict the value in 2009.
(b) How much difference (numerical) is there between the estimated and actual 2009 values? Is this an underestimate or overestimate?
(a) First find the compounded percentage increase p between 1995 and 2005.
7446 = 5471 (F/P,p,10)
1.36099 = { (1+p) }^{ 10 }
\quad p = 0.0313 or 3.13 % per year
Predicted index value in 2009 = 7446(F/P,3.13%,4)
\quad \quad \quad\quad \quad \quad \quad \quad \quad \quad \quad \quad = 7446{ (1+0.0313) }^{ 4 }
\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad\quad = 8423
(b) Difference = 8570 – 8423
\quad \quad \quad \quad\quad = 147 (underestimate)