Answer:
a. Depreciation function
F = (1-r)^t
b, $17,357
c. 11.6%
Step-by-step explanation:
a. Firstly, we are told to find the linear depreciation function. This means an equation that shows how the depreciation is playing out.
To get this, we shall go the exponential way;
Let F = future value of the car, P = Present value of the car, r = percentage of depreciation and t = time or number of years
So the depreciation function will be;
F = P(1 - r)^t
c. Let’s calculate the rate at which it is depreciating
According to our formula, F = $19,645 while P = $25,125 and t = 3
The depreciation function is;
F = P(1-r)^t
So substituting these values, we have;
19,645 = 25,125(1-r)^2
Divide both sides by 25,125
19645/25125 = (1-r)^2
(1-r)^2 = 0.782
Find the square root of both sides;
1-r = √0.782
1-r = 0.884
r = 1-0.884 = 0.116 which is same as 11.6%
b. We want to find the cost of the car in 3 years
We use the same depreciation function;
F = P(1-r)^t
where in this case F = ? , P = 25,125 , r = 0.116 and t = 3
Substituting these values, we have
F = 25125(1-0.116)^3
F = 25125(0.884)^3 = $17,357
