A truck depreciates in value by 15% per year. If the truck is valued at $ 40 000 on August 1, 2010, what will its value be to the nearest dollar on August 1st 2016?
value = 40000(.85)^6 = 15085.98 or $15086
To find the value of the truck on August 1st, 2016, we need to determine how much it depreciates each year and apply that depreciation for the number of years from 2010 to 2016.
The truck depreciates by 15% per year, which means its value is reduced to 85% (100% - 15%) of its original value every year.
To calculate the value of the truck on August 1st, 2016, we can use the following steps:
1. Calculate the number of years between August 1, 2010, and August 1, 2016. In this case, it is 6 years.
2. Calculate the depreciated value for each year by multiplying the previous year's value by 0.85 (85%). Start with the initial value of $40,000 and repeat this calculation for each year until 2016.
Let's break it down:
Year 1 (2010-2011):
Value = $40,000 * 0.85 = $34,000
Year 2 (2011-2012):
Value = $34,000 * 0.85 = $28,900
Year 3 (2012-2013):
Value = $28,900 * 0.85 = $24,565
Year 4 (2013-2014):
Value = $24,565 * 0.85 = $20,880
Year 5 (2014-2015):
Value = $20,880 * 0.85 = $17,748
Year 6 (2015-2016):
Value = $17,748 * 0.85 = $15,086.80
Therefore, the value of the truck on August 1st, 2016, will be approximately $15,087 to the nearest dollar.