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.
do you mean the annual rate?
19400(1-r)^3 = 12105
r = 0.145 = 14.5%
thanks
To calculate the rate of decline in the value of the car, we need to find the difference between the initial value and the final value, and then divide it by the initial value. Here are the steps to solve this problem:
1. Calculate the difference between the initial value and the final value:
Difference = Initial value - Final value
Given that the initial value (sticker price) is $19,400 and the final value is $12,105:
Difference = $19,400 - $12,105
2. Divide the difference by the initial value:
Rate of decline = Difference / Initial value
Rate of decline = ( $19,400 - $12,105 ) / $19,400
Now, let's calculate step by step:
Difference = $19,400 - $12,105
Difference = $7,295
Rate of decline = $7,295 / $19,400
Using a calculator or performing the division manually, we get:
Rate of decline = 0.375
Finally, we can express the rate of decline as a percentage by multiplying it by 100:
Rate of decline = 0.375 * 100
Rate of decline = 37.5%
Therefore, the rate of decline in the value of the car is 37.5%, which means the car lost 37.5% of its value over the three-year period.