4C  Credit Cards


credit cards

A credit card loan is an open-ended loan - that is, there is no specific date for paying off the loan. You receive a monthly statement, and each month you may pay off the entire balance or only part of the balance. Usually there is a minimum monthly payment you must make, but this payment can in many cases be just a small part of your outstanding balance. If you are diligent every month and pay off the entire balance on your card before the due date, then there is no finance charge. However, if you fall behind and do not pay your entire bill regularly, additional finance charges will be added. In fact, it is to the bank's benefit if you do not pay off your entire bill every month, as credit card finance charges can be a lucrative source of bank income. Most banks would probably be quite happy to see you continue from month to month making only the minimum payment, as long as you do not get far enough behind to exceed your credit limit.

Interest charges on credit card accounts are generally significantly higher than on ordinary loans. Some introductory card rates can be low for six months or a year, but after the smoke clears your annual credit card interest rate will probably settle somewhere in a range from 15% to 20%. The high interest rate is no problem if you pay off your entire balance every month, but if you find you are carrying an outstanding balance from month to month you would probably be better off getting a conventional loan in order to pay off your credit card debt. Of course credit cards are convenient, and sometimes even necessary if you want to rent a car or a hotel room. However, the akamai consumer will not use credit cards as mainly a quick and easy way to borrow money.

There are various ways that financial institutions can calculate interest on credit card accounts. Some may base the finance charge on the previous month's outstanding balance, while others might base it on the previous month's balance minus any payments made in the interim. But probably the most common and fair method is the average daily balance method, in which, as the name implies, your interest charges are determined by your account's average daily balance over the previous month. It is this method that we will discuss in some detail.

  Let us suppose that a Big Island farmer, a little short on cash because of the drought, received a credit card statement for the period December 5 - January 4 listing the following activity:


  farmer
Previous Balance: $400
Dec. 8 - bought cattle feed: $440
Dec. 12 - made payment: $200
Dec. 20 - bought horse saddle: $130
Dec. 31 - bought fireworks: $126
 

Suppose also that the annual interest rate on his credit card is 20%, and that his bank uses the average daily balance method of computing interest. We will compute his average daily balance over the billing period, as well as his finance charges for that period.

It is helpful to organize the pertinent information in a table:


Time Interval # Days Balance
Dec 5 - Dec 7 3 $400
Dec 8 - Dec 11 4 $400 + $440 = $840
Dec 12 - Dec 19 8 $840 − $200 = $640
Dec 20 - Dec 30 11 $640 + $130 = $770
Dec 31 - Jan 4 5 $770 + $126 = $896
  Total Days : 31  

From Dec. 5 to Dec. 7 the farmer's balance was $400, until Dec. 8 when he purchased cattle feed for $440 and his balance went up to $840. The balance remained at $840 until Dec. 12, when the bank received his payment of $200. The balance then fell to $640 until Dec. 20 when his horse saddle charge of $130 raised it to $770. Finally, his balance remained constant until his fireworks bill of $126 appeared on Dec. 31, at which time the balance grew to $896, where it remained until the end of the billing period.

To compute the average daily balance, we add the balances on each of the individual 31 days, and then divide the sum by 31. Since his balance was $400 for 3 days, we must 3 times add $400. Likewise, we must 4 times add $840, 8 times add $640, 11 times add $770, and 5 times add $896. Then we divide the entire sum by 31. Thus the average daily balance for the billing period is the quantity


calculation

This average figure is taken as the principal P for the billing period - that is, for billing purposes it is assumed that the farmer borrowed $730 for the entire period.

To calculate the interest charged to the farmer for the period of 31 days, we use the simple interest formula. As the time of the loan is given in days, it is easiest to work in days and change the annual interest rate to a daily rate. The annual rate is 20%, and a year has 365 days, so the daily interest rate charged by the bank is


calculation

The time period is t = 31 days, and consequently the farmer's interest for the billing period is


calculation

This interest amount of $12.40 will be added to the farmer's unpaid balance, and it will be listed as a finance charge. His new balance will be the last balance plus the finance charge, or


$896.00 + $12.40 = $908.40  .



EXERCISES 4C


  1. Ricardo
    On his Gold Visa card statement for the period June 15 - July 14, Ricardo saw the following items:

    Previous Balance: $873
    June 20 - hood ornament for Cadillac: $180
    June 30 - made payment: $500
    July 3 - dinner for two at Michel's: $245
    July 8 - new Armani suit: $960

    Ricardo's bank charges an 18% annual interest rate on the card, and uses the average daily balance method of computing interest. Calculate


    1. Ricardo's average daily balance for the period,
    2. the finance charge for the period,
    3. Ricardo's new balance at the end of the period.

    (Remember: June has only 30 days!)

  2. A young couple from Nebraska, upon returning from their Hawaiian vacation, found that their Master Card activities for the statement period August 5 - September 4 were as follows:

    dancers at PCC  
    Previous Balance: $431
    Aug. 10 - Polynesian Cultural Center tickets: $123
    Aug. 14 - Hilo Hattie bill: $63
    Aug. 24 - made payment: $200
    Aug. 30 - rental car bill: $410
    Sept. 2 - ABC store bill: $33

    Their new balance at the end of the statement period was $867.44. Calculate
    1. their finance charge for the period,
    2. their average daily balance for the period,
    3. the annual interest rate on their credit card account.