determine the value of the vehicle

Question

A vehicle is purchased for $32000. If the vehicle depreciates (loses value) at a rate of 17 percent per year, determine the value of the vehicle after 3 years. Round answer to the nearest cent.

$____

Answer 1

we can clearly see the interest applied is compounded interest so we will apply formula of CI (compound interest)

we know that CI = P(1-r/n)^nt

where p = initial principal = 32000

r = rate in percent = -17%

n = number of time the rate apply within given period = 1

t = time period = 3 years

so CI = 32000×(1-(17/100)/1)^1×3 ⇒CI = 32000×(1-0.17)³

i.e CI = 32000×(0.83)³ ⇒ CI = 32000×(0.5717)

hence CI = 18297.184 ≈ 18297.18

so price of vehicle after 3 years is $18297.18 or 18297 dollar and 18 cents

Answer 2

Function

f(t) = 32000(1-0.17)^t = 32000(0.83)^t

If the number of years passed is t=3:

f(3) = 32000(0.83)³ ≈ $18297.19

Hope this helped!