ben bought a car for $20,000 in 2003. The car depreciates at a constant rate of 21% per year . Find the price of the car in the year 2010 . Round to nearest dollar
the car is worth only .79 of previous year's value.
After 7 years, therefore, it is worth
20000*.79^7 = 3840.78
To find the price of the car in the year 2010, we need to calculate how much it depreciates each year from 2003 to 2010.
Step 1: Calculate the depreciation amount for each year:
Depreciation amount = Car price * Depreciation rate
In 2004:
Depreciation amount = $20,000 * 21% = $4,200
In 2005:
Depreciation amount = $20,000 * 21% = $4,200
In 2006:
Depreciation amount = $20,000 * 21% = $4,200
In 2007:
Depreciation amount = $20,000 * 21% = $4,200
In 2008:
Depreciation amount = $20,000 * 21% = $4,200
In 2009:
Depreciation amount = $20,000 * 21% = $4,200
In 2010:
Depreciation amount = $20,000 * 21% = $4,200
Step 2: Subtract the total depreciation amount from the original price of the car to find the price in 2010:
Price in 2010 = Original price - Total depreciation
Total depreciation = $4,200 + $4,200 + $4,200 + $4,200 + $4,200 + $4,200 + $4,200 = $29,400
Price in 2010 = $20,000 - $29,400 = -$9,400
Since the result is negative, it means that the car has been fully depreciated and has no value. So, the price of the car in the year 2010 is $0 (rounded to the nearest dollar).
To find the price of the car in the year 2010, we need to calculate the depreciation each year from 2003 to 2010 and then subtract it from the original price.
First, let's calculate the depreciation rate per year. The car depreciates at a constant rate of 21% per year. This means that each year, the car's value decreases by 21%.
To find the price of the car in a specific year, we multiply the previous year's price by (1 - depreciation rate).
Starting with the price of $20,000 in 2003, we can calculate the price in 2004 as follows:
Price in 2004 = $20,000 x (1 - 0.21) = $20,000 x 0.79 = $15,800
Proceeding in the same manner, we can find the prices in subsequent years as follows:
Price in 2005 = $15,800 x (1 - 0.21) = $15,800 x 0.79 = $12,442
Price in 2006 = $12,442 x (1 - 0.21) = $12,442 x 0.79 = $9,814
Price in 2007 = $9,814 x (1 - 0.21) = $9,814 x 0.79 = $7,746
Price in 2008 = $7,746 x (1 - 0.21) = $7,746 x 0.79 = $6,114
Price in 2009 = $6,114 x (1 - 0.21) = $6,114 x 0.79 = $4,829
Price in 2010 = $4,829 x (1 - 0.21) = $4,829 x 0.79 = $3,805
Rounding to the nearest dollar, the price of the car in 2010 is $3,805.