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A new car lists for $18,940 and depreciates by 45% per year. Find its value after the following amounts of time. (Round your answers to the nearest dollar.)

(a) 2 years

(b) 3 months

Answer :

Final answer:

A car that costs $18,940 and depreciates by 45% per year would be worth $5,729 after 2 years and $17,208 after 3 months based on calculations of yearly and prorated depreciation.

Explanation:

This question is about calculating the depreciated value of a car. Given that the initial price of the car is $18,940 and it depreciates by 45% per year, to calculate the value after a certain period of time, you need to subtract the depreciation from the initial price.

(a) For 2 years, you need to calculate the depreciation for each year and subtract it from the preceding year's value. So, after the first year, it would be $18,940 - ($18,940*0.45) = $10,417(rounded to nearest dollar). For the second year, it would be $10,417 - ($10,417*0.45) = $5,729

(b) For 3 months, since it's less than a year, the car has depreciated only for that period out of the year. So it would be $18,940 - ($18,940 * 0.45 * 3/12) = $17,208. Thus, the car is worth $5,729 after 2 years and $17,208 after 3 months.

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