A musician buys a piano for $5,000. If the value of the piano depreciates by 20% every year, what is the value of the piano after 5 years?
Remaining Amount $=I(1-r)^t$
Answer (2)
Identify the initial value I = $5000 , depreciation rate r = 0.20 , and time t = 5 years.
Substitute the values into the formula: R e mainin g A m o u n t = I ( 1 − r ) t = 5000 ( 1 − 0.2 ) 5 .
Calculate the remaining amount: R e mainin g A m o u n t = 5000 ( 0.8 ) 5 = 5000 × 0.32768 = 1638.4 .
The value of the piano after 5 years is $1638.40 .
Explanation
Understanding the Problem We are given that a musician buys a piano for $5,000. The value of the piano depreciates by 20% every year. We want to find the value of the piano after 5 years. The formula for the remaining amount is given by: R e mainin g A m o u n t = I ( 1 − r ) t where I is the initial value, r is the depreciation rate, and t is the time in years.
Identifying the Given Values We are given the following values: Initial value, I = $5 , 000 Depreciation rate, r = 20% = 0.20 Time period, t = 5 years
Calculating the Remaining Amount Now, we substitute the given values into the formula: R e mainin g A m o u n t = 5000 ( 1 − 0.2 ) 5 R e mainin g A m o u n t = 5000 ( 0.8 ) 5 R e mainin g A m o u n t = 5000 × 0.32768 R e mainin g A m o u n t = 1638.4
Final Answer Therefore, the value of the piano after 5 years is $1638.40.
Examples
Depreciation is a concept that applies to many assets, not just musical instruments. For example, when a company buys a vehicle for $25,000, they can use the same depreciation formula to estimate its value after a certain number of years. If the vehicle depreciates at a rate of 15% per year, its value after 3 years would be calculated as follows: Va l u e = 25000 ( 1 − 0.15 ) 3 = 25000 ( 0.85 ) 3 ≈ $15 , 340.63 This helps the company in financial planning, asset valuation, and tax calculations.
The value of the piano after 5 years, considering a depreciation rate of 20% annually, is approximately $1638.40. This was calculated using the formula for remaining value considering depreciation. By substituting the initial value, depreciation rate, and time into the formula, we found the final amount after 5 years.
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