Question

Hat is the value of the car two years after Fred buys it? Explain how you got your answer or show your work.

When will the car be worth less than $500,000? Explain or show your work

Answer 1

Explanation:

Since we don't have the information we need to fit this into an exponential equation, we will do it the simple way, using recursion. We will take the value of the car and subtract from it the depreciation, using the value at the end of one calculation as the initial value of the one following. Here's where it gets tricky, though. If the car's value at the end of a calculation is 80% of its initial value, then it depreciates 20%. Here is what the equation looks like after one year:

2,700,000 - .2(2,700,000) = 2,160,000

We subtracted away 20% of the initial to get the new initial. Now we use that value in the next recursion.

2,160,000 - .2(2,160,000) = 1,728,000

This is the value of the car after 2 years.

If we continue this process, we would find that after the 8th year, the car's value drops below 500,000 (namely, $452,984.83)