Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10%. The second car depreciates at an annual rate of 15%. What is the approximate difference in the ages of the two cars?

For each car, the remaining-value equation is (1 − depreciation rate)^t = 0.60. The 10% car takes about ln(0.60)/ln(0.90) = 4.85 years, while the 15% car takes about ln(0.60)/ln(0.85) = 3.14 years. Their ages differ by about 4.85 − 3.14 = 1.71 years, so the approximate difference is 1.7 years.

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