A certain vehicle loses 35% of its value each year.
Compute the value of the vehicle at the end of the 3rd year if the car has an initial value of $25,000
huhh???
value at end of year 1 = 25000(.65) = 16250
value at end of year 2 = 16250(.65) = 10562.50
value at end of year 3 = 10562.50(.65) = 6865.63
or in 1 step
value = 25000(.65)^3 = 6865.63
So much for you little trick, it is blatantly wrong.
Wait, just realized my mistake. It's actually 18,134 is the total loss of the value of the car. 25,000 - 18,134 = 6,866 (The car's value now)
1,250
A trick I've learned is by removing 10% each time, and that's easy because all you have to do is move the number over once to the right.
25,000 -> 2,500
2,500 * 3 = 7,500
10% of 25,000 is 2,500 / 2 = 1,250 Or 5% of 25,000
7,500 + 1,250 = 8,750
8750 x 3 = 26,250
26,250 - 25,000 = 1,250
How did you get 16,250? You probably need to recheck your answers.
To find the value of the vehicle at the end of the 3rd year, we can use the formula:
Value after years = Initial value × (1 - Rate)^Years
Given that the initial value is $25,000 and the rate of depreciation is 35% per year, we need to substitute these values into the formula.
Rate = 35% = 0.35 (since percentages are usually expressed as decimals)
Years = 3
Plugging these values into the formula:
Value after 3 years = $25,000 × (1 - 0.35)^3
To compute this, we need to perform the arithmetic operations step by step:
1. Calculate the rate of depreciation:
Value after 3 years = $25,000 × (1 - 0.35)^3
= $25,000 × (0.65)^3
2. Calculate (0.65)^3:
(0.65)^3 = 0.274625
3. Substitute this value back into the formula:
Value after 3 years = $25,000 × 0.274625
4. Calculate the final value:
Value after 3 years = $6,865.63
Therefore, the value of the vehicle at the end of the 3rd year is approximately $6,865.63.