Question

a new car is sold for its sticker value of $19,400. three years later the customer returns to the car dealership to trade the car in. she is told that her car now has a value of $12,105. what is the rate of decline in the value of the car? In your final answer, include all of your calculations.

Answer 1

Answer:

The rate of decline is $r=0.1455$  or $r=14.55\%$

Step-by-step explanation:

we know that

The  formula to calculate the depreciated value  is equal to  

$D=P(1-r)^{t}$  

where  

D is the depreciated value  

P is the original value  

r is the rate of depreciation  in decimal  

t  is Number of Time Periods  

in this problem we have  

$P=\ 19,400\\D=\ 12,105\\t=3\ years$

substitute in the formula above and solve for r

$\ 12,105=\ 19,400(1-r)^{3}$  

Simplify

$(12,105/19,400)=(1-r)^{3}$  

$(1-r)=\sqrt[3]{(12,105/19,400)}$

$r=1-\sqrt[3]{(12,105/19,400)}$

$r=0.1455$

Convert to percentage

$r=14.55\%$

Answer 2

Answer:

14.55

Step-by-step explanation: