Question

The manufacturer's suggested retail price (MSRP) for a particular car is $25,425, and it is expected to be

worth $11,730 in 5 years.
(a) Find a linear depreciation function for this car.
(b) Estimate the value of the car 7 years from now.
(c) At what rate is the car depreciating?
(a) What is the linear depreciation function for this car?
(Simplify your answer. Do not include the $ symbol in your answer.)

Answer 1

(a) The linear depreciation function of the car which gives the worth of the car y after a number of years, t is given as follows;

y = 25,425 - 2,739 × t

(b) The value of the car 7 years from now is $6,252

(c) $2,739 per year

Explanation:

The manufacture's suggested retail price (MSRP) for the car = $25,425

The amount the car is expected to be worth in 5 years = $11,730

(a) The linear depreciation is given as follows;

`Depreciation \ Per \ Year \ = (Cost \ of \, Asset - Salvage \ Value)/(Life \ of \, Asset \ in \ use)`

Where;

Cost of Asset = $25,425

Salvage Value = $11,730

Life of Asset in use = 5 years

We get;

`Depreciation \ Per \ Year \ = (\$ 25,425 - \$11,730)/(5) = \$2,739/year`

Therefore, the linear depreciation function, can be written as follows;

y - 25,425 = -2,739×(t - 0)

y = -2,739·t + 0 + 25,425 = 25,425 -2,739·t

y = 25,425 - 2,739 × t

Where;

y = The expected worth of the car after a given number of years

t = The number of years used for the calculation of the depreciation

(b) The value of the car 7 years from now is given by substitution as follows;

Whet t = 7, we have;

y = 25,425 -2,739·t = y = 25,425 -2,739 × 7 = $6,252

The value of the car 7 years from now = $6,252

(c)
`Depreciation \ Per \ Year \ = (\$ 25,425 - \$11,730)/(5) = \$2,739/year`

The car is depreciating at a rate of $2,739 per year.