The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

10.1 Credit Cards 423

Effective Date Activity Balance Days at Balance (Balance)(Days)

July 17 Start $815.49

July 21 $27.55 $843.04

July 28 $250.00 $593.04

August 5 $129.99 $723.03

August 8 $74.45 $797.48

Totals:

Once we have the information organized, we can focus on completing the last two columns.

The days between July 17 and July 21 can be calculated easily by subtracting: 21  17 


4 days. Similarly, we fi nd that there are 7 days between July 21 and 28.

Finding the days between July 28 and August 5 is a bit trickier, since the crossover between

months makes simply subtracting impossible. This can be done easily in either of two ways.

One approach would be to count the days in July and August separately, and then add the

total. This is essentially the approach we used in Chapter 1 when similar situations arose with

the dates of notes.

A second, equally effective, approach would be to just pretend that the month of July con-

tinued. Since August 5 is 5 days beyond the end of July, we think of it as “July 36th”. We can

then just subtract 36  28 to get a total of 8 days.

The remaining dates all fall within the month of August, so we can go back to simply sub-

tracting. 8  5 
 3 days between August 5 and 8, and 17  8 
 9 days between August

8 and the end of the billing month. Once we have calculated the days for each balance,

we can also complete the last column by multiplying each row’s balance by its days at that

balance.

Completing the table, we get:

Effective Date Activity Balance Days at Balance (Balance)(Days)

July 17 Start $815.49 4 $3,261.96

July 21 $27.55 $843.04 7 $5,901.28

July 28 $250.00 $593.04 8 $4,744.32

August 5 $129.99 $723.03 3 $2,169.09

August 8 $74.45 $797.48 9 $7,177.32

Totals: 31 $23,253.97

Completing the ADB calculation by dividing the column totals, we get:

ADB 

$23,253.97

___ 31
$750.13

Calculating Credit Card Interest

Once we have the ADB, calculating the credit card interest is fairly straightforward. Since no

compounding occurs within the billing month, we can use the simple interest formula, with the

ADB as the principal. One potential sticky point is the time. The time period can be thought

of either as 1 month (hence T 
 1/12) or as the actual number of days in the billing period, in

which case T 
 (number of days in the billing period)/(number of days in the year). In most

cases, the interest with time is calculated by using the number of days in the billing period.^2

Example 10.1.2 Suppose that Joanna’s credit card (from Example 10.1.1) carries

an interest rate of 15.99%. How much interest would she owe for the billing month

from Example 10.1.1?

(^2) In all of the examples and problems in this section, we will use the simplifi ed exact method and assume 365 days
per year. During leap years, 366 days would be used, but we will assume that the year is not a leap year in the
examples and exercises of this section.