16 Chapter 1 Simple Interest
Example 1.2.5 Calculate the simple interest due on a 120-day loan of $1,000 at 8.6%
simple interest in three different ways: assuming there are 365, 366, or 365.25 days in
the year.365 days: I PRT ($1,000)(0.086)(120/365) $28.27
366 days: I PRT ($1,000)(0.086)(120/366) $28.20
365.25 days: I PRT ($1,000)(0.086)(120/365.25) $28.26This example shows that, while the number of days used does indeed make a difference,
the difference is quite small—a few pennies on a $1,000 loan. The differences are not large
but they can be annoying, causing discrepancies that are small enough to not matter much
but still large enough to be frustrating.
Interest that is calculated on the basis of the actual number of days in the year is called
exact interest; calculating interest in this way is known as the exact method. For the
sake of simplicity (and sanity), it is not uncommon to adopt the rule of always assum-
ing that a year has 365 days, since that is the more common number of days for a year
to have, and using 365 or 366 makes very little difference. Always using a 365-day year
may be referred to as the simplified exact method. In this text we will adopt the rule that
unless otherwise specified, interest is to be calculated using the simplified exact method
(i.e. 365 days per year).Example 1.2.6 Calculate the simple interest due on a 150-day loan of $120,000 at
9.45% simple interest.Following the rules stated above, we assume that interest should be calculated using 365 days
in the year.I PRT
I ($120,000)(0.0945)(150/365)
I $4,660.27Loans with Terms in Days—Bankers’ Rule
There is another commonly used approach to calculating interest that, while not as true
to the actual calendar, can be much simpler. Under bankers’ rule we assume that the year
consists of 12 months having 30 days each, for a total of 360 days in the year.
Bankers’ rule was adopted before modern calculators and computers were available.
Financial calculations had to be done mainly with pencil-and-paper arithmetic. Bankers’
rule offers the desirable advantage that many numbers divide nicely into 360, while very
few numbers divide nicely into 365. This simplifies matters and reduces the tediousness
of calculations without sacrificing too much accuracy. Five days out of an entire year does
not amount to much.
Since financial calculations today are mostly done with calculators and computers,
bankers’ rule has lost a lot of its appeal. There actually still are some reasons to like bank-
ers’ rule (we will run into a few later on) even with technology to do our number crunching,
but by and large bankers’ rule has been fading away. But it has been widely used for a very
long time and, thanks to its longstanding status as a standard method, remains in common
use today.
Calculations with bankers’ rule really aren’t done any differently than with the exact
method. The only difference is that you divide the days by 360.Example 1.2.7 Rework Example 1.2.5 using bankers’ rule:Calculate the simple interest due on a 120-day loan of $10,000 at 8.6% simple interest using
bankers rule.360 days: I PRT ($1,000)(0.086)(120/360) $28.67Comparing this example to the results of Example 1.2.5, we can see that, while bankers’
rule does make a difference, the difference is not enormous.