A company replaces their cars every 6 years. A car is worth $13520 after 2 years. The company uses a depreciation rate of 35% a year.
a) How much will the car be worth when the company replaces it?
b) How much did the car cost when it was purchased?
if the initial value is v,
v - .35(2) = 13520
Now, knowing v, after n years the car is worth
v(1 - .35n)
Note that the car is fully depreciated after only 3 years, if the depreciation is 35% of the full value each year.
To answer these questions, we need to calculate the annual depreciation rate and the number of years the car is used before being replaced. Let's break it down step by step:
a) How much will the car be worth when the company replaces it?
First, we need to determine the depreciation rate per year. Given that the car depreciates by 35% each year, we can calculate the annual depreciation rate by dividing 35% by 100: 35% / 100 = 0.35.
Next, we'll find the number of years the car is used before being replaced. Since the company replaces their cars every 6 years, we can subtract the number of used years to find the remaining years: 6 years - 2 years (already used) = 4 years.
Now, we'll calculate the value of the car after the remaining 4 years of depreciation. To do this, we'll multiply the initial value of the car by the depreciation rate raised to the power of the number of remaining years:
Value = Initial value * (1 - Depreciation rate)^(Number of remaining years)
Using the given values:
Initial value = $13520
Depreciation rate = 0.35
Number of remaining years = 4
Value = $13520 * (1 - 0.35)^4
Calculating the value gives us:
Value = $13520 * (0.65)^4
Value ≈ $7454.47
Therefore, the car will be worth approximately $7,454.47 when the company replaces it.
b) How much did the car cost when it was purchased?
To calculate the cost when the car was purchased, we can use the initial value and the total depreciation over the years.
The formula to calculate the cost when the car was purchased is as follows:
Cost when purchased = Value after depreciation + Total depreciation
Substituting the given values:
Value after depreciation = $13520
Total depreciation = Initial value - Value after depreciation
Total depreciation = $13520 - $7454.47
Total depreciation ≈ $6065.53
Now, we'll substitute the values back into the formula:
Cost when purchased = $13520 + $6065.53
Cost when purchased ≈ $19585.53
Therefore, the cost of the car when it was purchased was approximately $19,585.53.