A car enthusiast learns that a particular model of car, which costs $43,330 new, loses 17% of its value every year. How much will the car be worth in 9 years?If necessary, round your answer to the nearest cent.
Question
A car enthusiast learns that a particular model of car, which costs $43,330 new, loses 17% of its value every year. How much will the car be worth in 9 years?If necessary, round your answer to the nearest cent.
Solution
To solve this problem, we need to calculate the annual depreciation of the car's value over a period of 9 years.
Step 1: Understand the problem The car's value depreciates by 17% each year. This means that each year, the car is worth 83% (100% - 17%) of its value from the previous year.
Step 2: Set up the formula The formula to calculate the depreciation of an item over time is: V = P * (1 - r)^n where: V is the final value of the car P is the initial price of the car r is the rate of depreciation n is the number of years
Step 3: Plug in the values In this case, P = 43,330 * (1 - 0.17)^9
Step 4: Calculate the final value V = 43,330 * 0.174 V = $7,539.42
So, the car will be worth approximately $7,539.42 in 9 years.
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