richard parker buys a new car for 15,000. the value of the car depriciates at about 16% each year. how much is the car worth after 5 years?

Question

Richard parker buys a new car for 15,000. the value of the car depreciates at about 16% each year. how much is the car worth after 5 years

Answer 1

If the car depreciates at a rate of 16% each year, then each year the car is worth only 84% = 0.84 of the former year's price. The situation can be modeled using an exponential rate of growth (or, in this case, decay) equation:

 

V(t) = a(r)^t

 

V(t) is the value of the car, a is the initial value of the car, r is the rate of growth, and t is the number of years that have gone by. For you, a = 15000, r = 0.84, and t = 5. Plug in and solve for V(t):

 

V(t) = 15000(0.84)⁵

V(t) = 15000(0.4182)

V(t) = 6273.18

 

The value of the car after 5 years is V(t) = $6,273.18.