Question

DeeDee Farrar purchased a new car 3 years ago for $33,500.00. Its current value estimate is $19.900.00. Annual variable costs this year were $995.60. The cost of insurance this year was 32,350.00, registration was $132.50. and loan interest totaled $1,080.00. She drove 13.540 miles this year. Compute the a) depreciation, b) annual fired costs, and c) cost per mile.

Answer 1

The annual depreciation of DeeDee Farrar's car is approximately $4,533.33, the annual fixed costs total $33,562.50, and the cost per mile comes to about $2.55.

Step-by-step explanation:

DeeDee Farrar purchased a new car 3 years ago for $33,500.00. Its current value estimate is $19,900.00. The annual variable costs this year were $995.60. The cost of insurance this year was $32,350.00, registration was $132.50, and loan interest totaled $1,080.00. She drove 13,540 miles this year.

To compute the depreciation of the car (a):
Depreciation = original purchase price - current value estimate = $33,500.00 - $19,900.00 = $13,600.00 over 3 years. To find the annual depreciation, we divide by 3, which equals approximately $4,533.33 per year.

To compute the annual fixed costs (b):
Annual fixed costs are the sum of insurance, registration, and loan interest costs = $32,350.00 + $132.50 + $1,080.00 = $33,562.50 for this year.

To compute the cost per mile (c):
Cost per mile is the sum of the annual variable costs and the annual fixed costs, divided by the total miles driven. Total annual costs = annual variable costs + annual fixed costs = $995.60 + $33,562.50 = $34,558.10. Therefore, cost per mile = $34,558.10 / 13,540 miles = approximately $2.55 per mile.

Answer 2

a) $4533.33 b)$8095.83 c) $0.67 per mile

1) Let's begin by writing down the formulas we are going to need for this problem:

Depreciation

`D=(Purchase\: Price -­ Today\: Value)/(Years\: Owned)`

And the cost per mile can be found using this:

`C=(Annual\: Variable\: Cost+\: Annual \: fixed\: cost)/(Number \: of \: miles)`

2) Now, let's plug into those formulas, the data we were told in the question.

Firstly, let's find the Depreciation.

a)

`(33500-19900)/(3)=(13600)/(3)=4533.33`

So that car suffered a depreciation of $4533.33 per period of 3 years

b) Annual fixed Costs

Let's add up all the fixed costs Dee Dee had to afford:

`2350+132.50+1080+4533.33=8095.83`

Note that all the costs (loan, registration ) and the depreciation comes as a fixed cost annually charged. So the fixed costs were $8,095.83

c) Cost per mile

We can find that using the 2nd formula above (on #1) note that the cost per mile is given as a ratio per the number of miles that were driven. So we've got:

`C=(995.60+8095.83)/(13,540)=0.671\approx0.67`

So the cost per mile is $0.67or 67 cents