Real World Math Part 2 – Depreciation

Previously we took a look at the down side of buying a new car with a loan. This time let’s do some further analysis using another cool formula to keep at the ready which can assist you with making purchase decisions. Works for cars, laptops, a new roof for your house, or any other thing you can buy that ages, goes obsolete or simply wears out.

We’ll use our $21,000 MSRP Toyota Corolla to look at asset depreciation. Granted, there are several factors that play into the depreciation of a new car. Milage, age, condition, adherence to a manufacturer’s maintenance schedule etc. all factor into a cars value at a certain point in its lifespan. However, for the purpose of analyzing rate of depreciation, we’ll leave out the other factors. In fact each manufacturer uses the various quality factors to calculate a vehicle’s affordability. Some cars are built to be inexpensive to own/maintain but have short lifespans, while others have strict and expensive maintenance schedules that are geared toward reliability and a long life.

The Problem:

Leaving all the other factors out, if our $21,000 Corolla depreciates 20% over the first year of its life, how many years would pass before the car’s value is equal to or less than the amount of interest we would have paid for the $19,500 we financed?

Cost of vehicle = $21,000.Total interest paid on vehicle = $6,189 Rate of depreciation = 20% subtracted from 100% leaves 80% or a factor of 0.80 for annual depreciation.

Formula: Cost x Rate^yrs = depreciated value

$21,000 x 0.8 (yrs)≤ $6,189

(Figuring out the value of the exponent will give the number of years before the car’s value is equal to or less than the amount of interest we paid on the loan)

0.8 (yrs)≤ $6,189÷$21,000 this gives 0.8 (yrs)≤ 0.2947

To calculate the number of years, we need to guess and check by plugging in some values for the exponent. You can even bracket the values of the exponents:

0.8 2 = .64 which is bigger than our 0.2947 and we’re looking for the same or less

0.8 8 = .1677 which is smaller, so the number of years will be somewhere in between.

Let’s try an exponent of 6: 0.8 6 = 0.2621 which is less than or equal to the figure in our formula.

The answer here is that the car’s value will be less than the interest paid on the loan after 6 years. Another way to look at this is when the car loan is paid at the end of 5 years, you’ll be driving a paid for car for 1 year before it has little or no value – if you sell it for $6,200 you’ll essentially be getting nothing since this is the money you already paid to the bank to finance it.

In part 3 of Real World math, we will look at compounding interest at rates other than annual (semi annual, quarterly, and monthly).