the general equation for depreciation is given by $y = a(1 - r)^t$, where $y =$ current value, $a =$…

the general equation for depreciation is given by $y = a(1 - r)^t$, where $y =$ current value, $a =$ original cost, $r =$ rate of depreciation, and $t =$ time, in years. the original value of a car is $24000. it depreciates 15% annually. what is its value in 4 years?

the general equation for depreciation is given by $y = a(1 - r)^t$, where $y =$ current value, $a =$ original cost, $r =$ rate of depreciation, and $t =$ time, in years. the original value of a car is $24000. it depreciates 15% annually. what is its value in 4 years?

Answer

Explanation:

Step1: Identify the values

$A = 24000$, $r=0.15$, $t = 4$

Step2: Substitute into the formula

$y=A(1 - r)^t=24000\times(1 - 0.15)^4$

Step3: Calculate $(1 - 0.15)^4$

$(1 - 0.15)^4=0.85^4=0.85\times0.85\times0.85\times0.85 = 0.52200625$

Step4: Calculate the current value $y$

$y=24000\times0.52200625 = 12528.15$

Answer:

$12528.15$