The Edisons are deciding whether or not to sell their 6-year-old SUV. Its original price was $39,289 and its annual rate of depreciation is 17%.A smaller, new car with better gas mileage will cost...

The Edisons are deciding whether or not to sell their 6-year-old SUV. Its original price was $39,289 and its annual rate of depreciation is 17%.

A smaller, new car with better gas mileage will cost $33,757.

A) How much is their old car worth today?

B) If the dealer will credit the Edisons with the dollar value of the car after 6 years' depreciation, how much additional money must they pay for the new vehicle?

 

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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The Edisons are deciding whether or not to sell their 6-year-old SUV. Its original price was $39,289 and its annual rate of depreciation is 17%.

As the value of the car depreciates by 17% every year, its present value is 39289*(1-0.17)^6 = $12845

The new car costs $33757. If the dealer were to credit the Edisons with the value of their old car after 6 years of depreciation, they would have to pay any extra amount equal to 33757 - 12845 = $20911.

The value of the SUV after 6 years with a depreciation of 17% is $12845. The extra that has to be paid for the new car is $20911.

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