Question

Terry just bought a used car with only 28,500 miles on it and it cost $8,200. Every year Terry expects to put another 14,000 miles on the car. Unfortunately, the car’s value will depreciate by 15% per year. How much will the car be worth when it has 100,000 miles on it? Explain your work.

Answer 1

It will take (100 -28.5)/14 ≈ 5.107 years to get to 100,000 miles. In that time the car will depreciate by a factor of 0.85^5.107, about 0.43605. The value at that time will be
.. $8200*0.43605 ≈ $3706

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The difference between 100k miles and 28.5k miles is 71.5k miles. It is "used up" at the rate of 14k miles per year, so the time it takes to do that is 71.5/14 ≈ 5.1 years.

Each year the car depreciates 15%. That is, its value is multiplied by 1 -15% = 0.85. In 5.1 years, the original value will be multiplied by 0.85^5.1. (Remember, exponentiation is repeated multiplication.)