A car purchased for $9,000 depreciates at a constant rate of 16.5%. What will be the value of the car in 6 years.

Question

A car purchased for $9,000 depreciates at a constant rate of 16.5%. What will be the value of the car in 6 years.

The Value in 6 years is $_________.

Round answer to 2 decimal places

Answer 1

Use the formula:

Value = P(1-r)ⁿ

P=9000

r = 0.165

n=6

Answer 2

First, note that 16.5% is equivalent to the decimal fraction 0.165; that is, after one year the car's value will be

$9000(1 - 0.165) = $9000(0.835) = $7785. After two years, the value will be $9000(0.835)(0.835), where 7785 has been replaced by its equivalent, (9000)(0.865). This process will continue until $9000 has been multiplied by 0.865, six times.

Simplify this process by writing $9000(0.865)⁶. Most calculators do this using the x^y key, entering 0.865, then the x^y key, then 6. The result is $3769.98.

This process can be adapted for any number of years, by simply replacing 6 with another integral value.