Stacy buys a used car for $22,000. If the value of the car depreciates by 18% every year, what is the value of the used car after 9 years?
Remaining Amount = [tex]I (1-r)^{ t }[/tex]
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Round your answer to the nearest whole number.
Answer (2)
Identify the initial value ( I = $22 , 000 ), depreciation rate ( r = 0.18 ), and time period ( t = 9 years).
Substitute the values into the formula: Remaining Amount = 22000 ( 1 − 0.18 ) 9 .
Calculate the remaining amount: Remaining Amount ≈ 3687.63 .
Round the remaining amount to the nearest whole number: \boxed{3688}.
Explanation
Understanding the Problem We are given that Stacy buys a used car for $22,000. The value of the car depreciates by 18% every year, and we want to find the value of the car after 9 years. The formula for the remaining amount is given by:
Remaining Amount = I ( 1 − r ) t
where:
I is the initial value of the car
r is the depreciation rate per year
t is the number of years
Identifying the Given Values We are given the following values:
Initial value of the car, I = $22 , 000
Depreciation rate, r = 18% = 0.18
Time period, t = 9 years
Substituting the Values into the Formula Now, we substitute the given values into the formula:
Remaining Amount = 22000 ( 1 − 0.18 ) 9
Calculating the Remaining Amount We calculate the remaining amount:
Remaining Amount = 22000 ( 0.82 ) 9
Remaining Amount = 22000 × 0.1676177076 ≈ 3687.589567
Rounding this to the nearest whole number, we get 3688.
Final Answer Therefore, the value of the used car after 9 years is approximately $3688.
Examples
Depreciation calculations are commonly used when determining the resale value of assets like cars or machinery. For instance, if a company buys a machine for $50,000 and it depreciates at a rate of 10% per year, understanding how to calculate its value after a certain number of years helps in financial planning, tax reporting, and making informed decisions about when to replace the equipment. This ensures accurate asset valuation and supports sound financial management.
After using the depreciation formula, the value of the car after 9 years rounds to approximately $8090. We calculated this using an initial value of $22,000 and a depreciation rate of 18% per year. Each step involved plugging the values into the formula and simplifying for the final amount.
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