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 $393,000 worth of assets after t years, that depreciate at 15% 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 7 years?

Vo = $393,000, b = 0.15, and the value after 7 years is $0.67
Vo = $393,000, b = 1.15, and the value after 7 years is $108,543.57
Vo = $393,000, b = 0.85, and the value after 7 years is $47,721.43
Vo = $393,000, b = 0.85, and the value after 7 years is $125,986.80

Answer 1

So, option d is correct i.e,

V₀ = $393,000, b = 0.85, and the value after 7 years is $125,986.80

Explanation:

The formula given is V(t)=V₀(b)^t

The value of V₀ (the actual worth) is:

V₀ = $393,000

The value of b is :

b= (1-15%) = (1-0.15) = 0.85

Value of assets after 7 years is:

t= 7, V₀ = $393,000, b=0.85

putting values in formula:

V(t) = Vo(b)^t.

V(7)= $393,000 * (0.85) ^ 7

V(7)= $393,000 * (0.320)

V(7)= $125986.80

So, option d is correct i.e,

Vo = $393,000, b = 0.85, and the value after 7 years is $125,986.80