The Mathematics of Money

74 Chapter 2 Simple Discount

(b) Though we already know that the price Ringo paid for the note was found with a 7¾%

simple discount rate, we also know from Section 2.2 that the simple interest rate will be

different. Look at the story from Ringo’s perspective:

$20,344.50 $21,600

9 months

From Ringo’s point of view, the principal is $20,344.50, the interest is $1,255.50 and the

term is 9 months.

I  PRT

$1255.50  ($20,344.50)(R)(9/12)

$1,255.50  $15,258.375(R)

R  8.23%

So we can conclude that Ringo earned a simple interest rate of 8.23%.

(c) Following the approach used in (a) and (b), we could draw a time line from Paul’s point

of view and then calculate the interest from there. That would give the correct answer, but

there is no need to go to that trouble. Paul agreed to pay 8% simple interest, and the fact

that his note was sold does not change that, no matter how many times it is sold. So the

simple interest rate that Paul pays is still 8%.

Even if a note is sold hundreds of times, we can always draw a time line from any indi-

vidual’s point of view and use that to calculate the simple interest rate that the individual

actually earned (or paid).

In Example 2.3.2, Tinker actually lost money. It is interesting to ask what sort of simple

interest rate that translates into.

Example 2.3.4 For the situation described in Example 2.3.2, calculate the simple

interest rate that Tinker actually earned.

$997.52 $993.90

74 days

In this case, instead of gaining interest, Tinker lost money. In other problems, we found the

amount of interest by subtracting, and following that approach we fi nd that his interest was

$993.90  $997.52  $3.62. The result is negative because Tinker lost money on the

deal. Proceeding to calculate his simple interest rate, we get:

I  PRT

$3.62  ($997.52)(R)(74/365)

$3.62  $202.232876712(R)

R  1.79%

While a negative interest rate may sound ridiculous, it actually describes this situation

quite well. It stands to reason that losing money on a loan could be expressed as “earning”

a negative interest rate.

Negative rates seem strange because we aren’t used to seeing them. You can imagine a

bank’s marketing nightmares trying to attract deposits by offering negative interest rates on

deposits! (“Come watch your account value drop!”) Of course charging negative interest rates

for loans might make the marketing department’s job easy (“Pay back less than you bor-

rowed!”), but it wouldn’t do much to help keep the bank in business. For these reasons, if no

others, negative interest rates are almost never actually used directly.^6 But when a note or other

investment is sold for less than was paid for it, negative rates can arise and do make sense.

Since Tinker did so poorly on this deal, it is worth asking how Chance made out.

(^6) Amazingly, this does happen sometimes. In the 1990s some Japanese savings accounts actually offered negative
interest rates. At the time the infl ation rate in Japan was essentially zero, and huge losses in the stock and real estate
markets left people willing to put up with “negative interest” in accounts where they felt their money would at least
be kept safe. While it might be psychologically diffi cult to watch your savings balance erode thanks to the interest it
“earns,” this really isn’t any sillier than depositing your money in a “safe” account paying 3% when prices are rising by
5%. In either case, the real value of your money is less at the end than at the start, and so you are losing either way.