As cars get older they are worth less than when they were new. This is called depreciation. Assume that you bought a new 2015 car for $13,700 and that it depreciates at approximately 20% per year. An equation that will model the value of your car v(t) where t is the number of years since 2015, is V(t)= 13,700(0.8)^t

(A) find V(1). Explain what it means in terms of the value of the car

(B) you plan to the sell the car when it reaches half of what you initially bought it for. In what year will you sell the car?

Depreciation is the depletion in the original purchase cost of the fixed asset over a period of time. It shows the reduction in the value of assets due to its usage, and wear and tear. it is a non-cash expense as there is no outflow of cash for recording the depreciation expense.

A) The V(1) is $10,960.

It is computed as follows:

[tex]\text{V}(1)=\text{Cost}-\text{Depreciation}\\\\=\$13,700-(\$13,700\times20\%)\\\\=\$13,700-\$2,740\\\\=\$10,960[/tex]

In terms of the value of car V(1) means the depreciated worth of the car after the end of 1st year.

B) The car must be sold in the year 2017. This is because if the car owner plans to sell the car when it reaches half of its purchase value, then in the year 2017 after depreciation the value of the car reaches to be approx 7,000-6,000.

The computation of the year of selling the car is shown in the image attached below.

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