A cyclist buys a bicycle for $1,500. If the value of the bicycle depreciates by 35% every year, what is the value of the bicycle after 3 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 = $1500 ), depreciation rate ( r = 0.35 ), and time period ( t = 3 ).
Substitute the values into the formula: Remaining Amount = 1500 × ( 1 − 0.35 ) 3 .
Calculate the remaining amount: 1500 × ( 0.65 ) 3 = 411.9375 .
Round the result to the nearest whole number: 412 .
Explanation
Understanding the Problem Let's analyze the problem. We are given the initial value of a bicycle, the annual depreciation rate, and the time period. We need to find the value of the bicycle after 3 years, rounding to the nearest whole number. The formula for the remaining amount after depreciation is given as Remaining Amount = I ( 1 − r ) t , where I is the initial value, r is the depreciation rate, and t is the time period.
Identifying Given Values We are given: Initial value of the bicycle, I = $1500 Depreciation rate, r = 35% = 0.35 Time period, t = 3 years
Substituting Values into the Formula Now, we substitute the given values into the formula: Remaining Amount = I ( 1 − r ) t = 1500 ( 1 − 0.35 ) 3 = 1500 ( 0.65 ) 3
Calculating the Remaining Amount Calculating the remaining amount: 1500 ( 0.65 ) 3 = 1500 × 0.274625 = 411.9375
Rounding to the Nearest Whole Number Rounding the result to the nearest whole number: 411.9375 ≈ 412
Final Answer Therefore, the value of the bicycle after 3 years is approximately $412 .
Examples
Depreciation calculations are commonly used in business and finance to determine the reduction in value of an asset over time. For example, a company might use depreciation to calculate the value of its equipment or vehicles for tax purposes. Understanding depreciation can help businesses make informed decisions about when to replace assets and how to manage their finances effectively. This concept is also applicable in personal finance, such as calculating the decreasing value of a car over the years.
The value of the bicycle after 3 years, considering a 35% depreciation each year, is approximately $412. This was calculated using the depreciation formula and rounding the result to the nearest whole number. The calculation involved the initial value of $1500 and applying the depreciation rate compounded over 3 years.
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