Question

Kevin and Claire have a house on several wooded acres. They heat their home largely by burning firewood that is delivered to them by the cord (a large quantity of wood). Kevin feels that, if they owned a wood splitter, he could cut up and split their own firewood and save the several hundred dollars per year they now spend on firewood. The cost of a good, gasoline-powered wood splitter is $4,000, which could be financed at seven percent. They figure that the machine would last eight years and then would be worthless. They also calculate that fuel for the machine would cost $30 per year and that repairs would average $50 per year over the eight years that they would own it. On average, what would their annual cost be to own the wood splitter?

NEED HELP URGENTLY!!!!!!!
A. $900

B. $80

C. $820

D. $860

Answer 1

The annual cost of owning the wood splitter, including depreciation, interest, fuel, and repairs, is $860.

This is calculated by adding the annualized initial cost, annual interest, repair, and fuel costs.

Therefore, the answer is D. $860.

Step-by-step explanation:

To compute the annual cost of owning the wood splitter for Kevin and Claire, we need to consider the initial cost, the interest on the financed amount, maintenance, and fuel costs over the lifespan of the wood splitter.

The initial cost of the wood splitter is $4,000. Since this cost is financed at a 7% annual interest rate, we will calculate simple interest over 8 years, which is the lifespan of the machine.

The interest per year is calculated as (Principal × Rate × Time) / Time of Loan.

Therefore, the interest per year for the wood splitter would be ($4,000 × 0.07 × 8) / 8

= $280.

We add the yearly fuel and repair costs to the interest cost: $280 (interest) + $30 (fuel) + $50 (repairs)

= $360 per year.

Finally, the annual depreciation cost of the wood splitter, assuming it is worthless after 8 years, is the initial cost divided by the number of years of use:

$4,000 / 8 = $500.

We add the depreciation to the annual running costs to get the total annual cost:

$500 (depreciation) + $360 (interest + fuel + repairs)

= $860.