8.4 Depreciation
The dollar value of anything that can be owned will change as time goes by. Some things,
like real estate and collectibles, are expected (or at least hoped) to go up in value over time.
We call that increase in something’s dollar value price appreciation. Other things, though,
become less valuable with use and the passing of time. Computers and electronics become
obsolete, used cars command lower prices than new ones (except for collectible cars), and
business equipment becomes less valuable as it ages and wears out while improved equip-
ment to do the same work comes on the market. The decline in something’s dollar value is
called depreciation.
Of course, the prices for things in a free economy are determined by the market—what a
willing buyer will pay a willing seller. The dollar value of a house, car, photocopier, compu-
ter, baseball card, tractor, hovercraft, or anything else for that matter will be whatever price
it can command in the open market, not the value computed by any mathematical formula.- A pharmacy receives a 27.5% trade discount on synthetic insulin, and sells it for 8.5% below list price. The pharmacy’s
retail price for a bottle of synthetic insulin is $67.43.
a. Find the list price.
b. Find the pharmacy’s cost per bottle.
c. Find the markup percent based on cost.
d. Find the gross profi t margin.E. Additional Exercises
- In Exercise 15, you were asked to fi nd the single equivalent discount for successive discounts of 15% and 35%. Then
the order was reversed, but the change did not affect the answer. Does the order of the discounts ever matter? Either
give an example where the single equivalent discount comes out differently when the order is switched, or provide a
convincing explanation of why order will never matter. - In the text of this section, we noted that sometimes series discounts are presented incorrectly. An advertisement
that says “take an additional 20% off our prices already cut by 50%” may mean a total 70% discount, even though
successive discounts of 50% and 20% are equivalent to a 60% discount.
From the customer’s point of view, this isn’t anything to complain about; you are getting a larger discount than you
would otherwise. However, the store is understanding the second discount. If the mathematically correct value for the
second discount is used, it would be a larger number.
Suppose that for a sale, prices being charged are actually discounted by 70%. The prices were already discounted by
50%. What is the correct percent for the second discount?
- Suppose that an invoice totals $12,350, excluding shipping costs. If the bill is paid within 15 days, there is a 2%
discount. If the payment is not made in full within 15 days, the seller will still apply the discount to the portion of the
invoice that is. If you pay $7,000 within the discount period, how much will you owe for the remaining bill? - Suppose that you have an invoice for $40,000. The bill is due in 60 days. If you pay within 15 days there is a 2%
discount. What is the simple interest rate equivalent to taking advantage of that discount offer?
362 Chapter 8 Mathematics of Pricing