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A new car is purchased for 20700 dollars. The value of the car depreciates at 11% per year. What will the value of the car be, to the nearest cent, after 11 years?

Question

A new car is purchased for 20700 dollars. The value of the car depreciates at 11% per year. What will the value of the car be, to the nearest cent, after 11 years?

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Solution

To solve this problem, we will use the formula for exponential decay, which is:

V = P * (1 - r)^t

where:

  • V is the final value of the car
  • P is the initial value of the car
  • r is the rate of depreciation
  • t is the time in years

Given in the problem: P = $20,700 r = 11% or 0.11 t = 11 years

Substituting these values into the formula, we get:

V = 20700 * (1 - 0.11)^11

Now, calculate the value inside the parentheses:

1 - 0.11 = 0.89

So, the formula becomes:

V = 20700 * (0.89)^11

Now, calculate the value of (0.89)^11, which is approximately 0.31381059609.

So, the formula becomes:

V = 20700 * 0.31381059609

Finally, calculate the value of 20700 * 0.31381059609, which is approximately $6496.88.

So, the value of the car after 11 years, to the nearest cent, will be $6496.88.

This problem has been solved

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