Question

Doug bought a new car for $25,000. He estimates his car will depreciate, or lose value, at a rate of 20% per year. The value of his car is modeled by the equation V = P(1 – r)t, where V is the value of the car, P is the price he paid, r is the annual rate of depreciation, and t is the number of years he has owned the car. According to the model, what will be the approximate value of his car after 4 and one-half years?.

Answer 1

The value of his car after 4 and one-half years is $9159.

Given

Doug bought a new car for $25,000.

He estimates his car will depreciate, or lose value, at a rate of 20% per year.

The value of his car is modeled by the equation V = P(1 – r)t,

Where V is the value of the car, P is the price he paid, r is the annual rate of depreciation, and t is the number of years he has owned the car.

What is depreciation?

Depreciation is a kind of accounting method that is utilized for the allocation of the physical asset cost in the context of its life expectancy or its usefulness.

The value of his car is modeled by the equation;

$\rm V = P(1 - r)^t$

Where the value of p = 25,000 and r is 20% = 0.20 and time is er 4 and one-half years = 4.5 years.

Substitute all the values in the formula;

$\rm V = P(1 - r)^t\\\\V = 25000(1-0.20)^{4.5}\\\\V = 25000(0.80)^{4.5}\\\\V = 25000 \times 0.366\\\\V = 9159$

Hence, the value of his car after 4 and one-half years is $9159.

To know more about Depreciation click the link given below.

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