Question

A new car is purchased for 16500 dollars. The value of the car depreciates at 5.75% per year. What will the value of the car be, to the nearest cent, after 5 years?

Answer 1

The value of the car after 5 years if it depreciates at the rate of 5.75% is 12,271.3

Exponential equations

The standard exponential equation is expressed as:

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

• P is the initial cost
• r is the rate
• t is the time

Given the following

P = 16500
r = 5.75% = 0.0575
t = 5 years

Substitute

P(t) = 16500(1-0.0575)^5
P(5) = 16500(0.7437)

P(5) = 12,271.3

Hence the value of the car after 5 years if it depreciates at the rate of 5.75% is 12,271.3

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