You buy a used car for $6599. Its value decreases by 12% every year. What is the value of the car after five years? Round your answer to the nearest hundredth

Answer 1

Car value after 5 years = (principal)(100 - %)^t

^{car value after 5 years = y}

^{principal = 6599}

^{% = 0.12}

^{t = 5 years}

y = (6599)(1 - 0.12)⁵

y = (6599)(0.88)⁵

y = (6599)(0.5277319168)

y = 3,482.5029189632

answer = 3,482.50

Answer 2

Key here is to state the problem as a multiplier: losing 12% per year can be stated as multiplying by .88 every year.

After one year, the value is .88P if P is the original price

after two years, the value is .88(.88P) = (.88)² P

In your case, after the 5th year, the value will be (.88)⁵ P.

Hope that helps.

Answer 3

Use the depreciation formula:

FV = PV (1+ r/100)ⁿ

where FV = future value, pv = present value, r = the annual depreciation rate (neg.) and n = no. of years.

FV = 6599 (1+ -12/100)⁵

Remember order of operations (PEMDAS):.

FV = 6599 ( .88)⁵

FV = 6599(.5277...)

FV after 5 years = 3482