Question

Alex purchased a new car for $28,000. The car's value depreciates 7.25% each year. What will be the value of the car 5 years after it is purchased? Round your answer to the nearest dollar.

Answer 1

First Year - $28,000 with a 7.25% depreciation = 28000 * 7.25% = 2,030 - 28000 = $25,970 Second Year - $25,970 with a 7.25% depreciation = 25970 * 7.25% =1883 - 25970 = $24,087 Third Year - $24,087 with a 7.25% depreciation = 24087 * 7.25% = 1746 - 24087 = $22,341 Fourth Year = $22,341 with a 7.25% depreciation = 1620 - 22341 = $20,721 Fifth Year = $20.721 with a 7.25% depreciation = 1502 - 20721 = $19,219

Answer 2

For this case we have a function of the form:

$y = A * (b) ^ x$

Where,

A: initial value

b: decrease rate

x: time in years

Substituting values we have:

$y = 28000 * (0.9275) ^ x$

For the year number 5 we have:

$y = 28000 * (0.9275) ^ 5\\y = 19219$

Answer:

the value of the car 5 years after it is purchased will be:

$y = 19219$