An automobile purchased for 24000 is worth 2100 after 8 years. Assuming that the car's value depriciated steadily from year to year, what was it worth at the end of the third year?
24000-8x=2100
2737.5 each year
2400(1+i)^-8 = 2100
.
.
1+i = 1.01683
then 2400(1.01683)^-3 = $2282.78
To find out the worth of the automobile at the end of the third year, we can calculate its annual depreciation and subtract it from the initial value.
Given:
Initial value (after purchase) = $24000
Value after 8 years = $2100
To calculate the annual depreciation, we need to determine the total depreciation over 8 years and divide it by the number of years.
Total depreciation = Initial value - Value after 8 years
Total depreciation = $24000 - $2100
Total depreciation = $21900
Annual depreciation = Total depreciation / Number of years
Annual depreciation = $21900 / 8
Annual depreciation = $2737.50
Now that we know the annual depreciation, we can calculate the worth of the automobile at the end of the third year.
Worth at the end of the third year = Initial value - (Annual depreciation * Number of years)
Worth at the end of the third year = $24000 - ($2737.50 * 3)
Worth at the end of the third year = $24000 - $8212.50
Worth at the end of the third year = $15787.50
Therefore, the automobile was worth $15,787.50 at the end of the third year.