Question

For accounting purposes, the value of assets (land, buildings, equipment) in a business are depreciated at a set rate per year. The value, V(t) of $408,000 worth of assets after t years, that depreciate at 18% per year, is given by the formula V(t) = Vo(b)t. What is the value of Vo and b, and when rounded to the nearest cent, what are the assets valued at after 8 years?

Answer 1

This is exponential decay of the form:

f=ir^t, f=final value, i=initial value, r=rate, t=time in this case:

V(t)=408000((100-18)/100)^t

V(t)=408000(0.82)^t so

Vo=408000 and b=0.82

....

V(8)=408000(0.82)^8

V(8)=$83400.95 to nearest cent