Question

Please help! How on earth do I do this? In the year 2015, Anna bought a new car for $36,000. In 2017, she was told that the value of her car was $25,000 due to depreciation. She is told that the value of her car depreciates linearly.
Find a function V(t) which gives the value of the car t years after the year 2015.
In 2018, Anna is told that she will be given $15,000 for her car if she decides to trade it in for a new car. Use the function from part (1) above to determine the value of her car in 2018.
Is the $15,000 value fair based on what she was told about linear depreciation? Explain your answer?

Answer 1

Part A

Purchase Value of Anna's Car in 2015 = $36,000

Depreciated Value of Anna's Car in 2017 = $25,000

We know that the value of the car is depreciating linearly.

From the above data, we can see that the value of the car has reduced by $36,000-$25,000 = $11,000 over 2 years.

⇒ Per year the value has been depreciated by $\frac{11000}{2}$

⇒ Per year the value has been depreciated by $5,500

So if the value of a car in 2015 is V₀ then value of the car after t years can be determined by the below function:

V (t) = V₀ - (t*5,500), where t indicates the years passed since 2015

OR V (t) = 36,000 - (t*5,500), where t indicates the years passed since 2015

Part B

Suggested value of Anna's car for trade in option in 2018 = $15,000

In 2018, 3 years would have been passed since 2015. Using the value of t = 3 in the function determined in Part A:

V(3) = V₀ - (3*5,500)

⇒ V(3) = 36,000 - (16,500)

⇒ V(3) = $19,000

From the above calculations, we can see that the value of the car in 2018 should be $19,000, however the suggested value for trade in is indicated as $15,000 which is lower than what the value of the car should be. Hence, basis linear depreciation, the $15,000 value is not fair for the car in 2018.