An automobile purchased for $31,000
is worth $2800
after 6
years. Assuming that the car's value depreciated steadily from year to year, what was it worth at the end of the third year?
the depreciation factor is r, where
r^6 = 2800/31000 = 0.090
The value after 3 years is thus
31000 * r^3
= 31000 * √.09
= 31000 * .3
= 9300
To find out the worth of the car at the end of the third year, we need to determine the annual depreciation rate and subtract it from the initial value of the car.
First, let's calculate the total depreciation of the car over 6 years:
Total depreciation = Initial value - Final value
Total depreciation = $31,000 - $2,800
Total depreciation = $28,200
Now, we need to find the annual depreciation rate:
Annual depreciation rate = Total depreciation / Number of years
Annual depreciation rate = $28,200 / 6
Annual depreciation rate ≈ $4,700
To determine the worth of the car at the end of the third year, we multiply the annual depreciation rate by the number of years (3) and subtract this amount from the initial value of the car:
Worth at the end of the third year = Initial value - (Annual depreciation rate * Number of years)
Worth at the end of the third year = $31,000 - ($4,700 * 3)
Worth at the end of the third year = $31,000 - $14,100
Worth at the end of the third year = $16,900
Therefore, the car was worth approximately $16,900 at the end of the third year.