Question

A new car is purchased for 20000 dollars. The value of the car depreciates at 12. 5% per year. What will the value of the car be, to the nearest cent, after 11 years?.

Answer 1

To solve the problem we need to know about depreciation.

Formula of Depreciation

The formula of depreciation is given as,

$A = P(1-r)^t$

where,

A is the value of an object after t years of time,

P is the value of the object at the beginning, and

r is the rate of depreciation.

The value of the car after 11 years is $4,603.81.

Explanation

Given to us

• Cost of Car at the beginning, p = $20,000
• Rate of depreciation, r = 12.5%
• Time, t = 11 years

Value of the car after 11 years

Substituting the values in the formula of depreciation,

$A = P(1-r)^t$

Value of the car after 11 years = $P(1-r)^n$

                                                 $= \ 20,000(1-0.125)^{11}\\\\ = \ 20,000\times 0.23\\\\ = \ 4,603.822 \approx \ 4,603.81$

Hence, the value of the car after 11 years is $4,603.81.

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