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A new car is purchased for 20800 dollars. The value of the car depreciates at 10.75% per year. What will the value of the car be, to the nearest cent, after 13 years?

Question

A new car is purchased for 20800 dollars. The value of the car depreciates at 10.75% per year. What will the value of the car be, to the nearest cent, after 13 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 = $20,800 r = 10.75% = 0.1075 (as a decimal) t = 13 years

Substitute these values into the formula:

V = 20800 * (1 - 0.1075)^13

Now, calculate the value inside the parentheses:

1 - 0.1075 = 0.8925

So, the formula becomes:

V = 20800 * (0.8925)^13

Now, calculate the exponent:

(0.8925)^13 ≈ 0.2635

So, the formula becomes:

V = 20800 * 0.2635

Finally, calculate the multiplication:

V ≈ 20800 * 0.2635 = $5482.80

So, the value of the car after 13 years, to the nearest cent, will be approximately $5482.80.

This problem has been solved

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