15.4: Credit Cards
- Page ID
- 185427
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- Read and understand the basic parts of a credit card statement.
- Compute interest, balance due, and minimum payment due for a credit card.
It can be difficult to get along these days without at least one credit card. Most hotels and rental car agencies require that a credit card is used. There are even a number of retailers and restaurants that no longer accept cash. They make online purchasing easier. And nothing contributes more to a good credit rating than a solid history of making credit card payments on time.
Being granted a credits card is a privilege. Used unwisely that privilege can become a curse and the privilege may be withdrawn. The more knowledge a cardholder has about the credit card industry, the better able credit accounts can be managed, and that knowledge may cause major adjustments to a cardholder’s lifestyle.
All credit cards are not equal, but they all represent consumers borrowing money, usually from a bank, to pay for needs and “wants.” As such, they are a type of loan, and your repayment may include interest.
There are many institutions and credit cards to choose from. Use caution as you shop around for a credit card that suits you. Your top concern is likely the interest rates on purchases and cash advances. But be careful to also read the small print regarding charges for late payments, and other fees such as an annual fee, where the credit card charges you (the cardholder) a fee each year for the privilege of using the cards. Many cards charge no such fee, but there are many that charge modest to heavy fees. Make sure to understand rules for reward programs, where the credit card issuer grants benefits based on one’s spending. Finally, once one applies for and is granted a credit card, pay attention to the credit limit the bank offers. Once a company is owed that much money, use of the card for purchases should be curtailed until some of the debt is paid off.
The interest rate will not matter if the balance is paid every month. When the balance is paid every month, there is NO INTEREST charged.
An interest rate will greatly depend on a credit score. Responsible use of credit cards will increase a credit score.
Credit Card Statements
Cardholders usually receive monthly statements and have 21 days to pay the minimum amount due. The statements itemize and summarize activity on the credit card for that statement’s billing period. The billing period for a credit card is generally a month long, but typically does not start and end on the first and last days of the month. The statement will include the current balance, interest rate, the minimum payment due, and the due date. Be aware that different companies produce statements that are laid out differently. The information will be clearly labeled though.
The due date is a top concern. Missing a due date is one of the worst things a cardholder can do financially, and this is by far the biggest downfall of owning a credit card. Not only is the cardholder subject to late fees, but when a payment is late more than once there is a high probability that the cardholder will be negatively reported to the credit bureaus, which can quickly erode a credit score. The figure below shows an excerpt from an actual statement from a Chase Bank Visa card, based on the current $668.25 balance.
Specifically pay attention to the late payment penalty and minimum payment warning statements. stating that if no other purchases are made and you continue making only the minimum payment, it will take 19 months to pay off the balance and you will pay $754.00. You can’t say you were not warned.
It is critical that you examine your statement every month because it is always a possibility that your account may have been compromised. If you should notice fraudulent charges on your statement, notifying the credit card company is often enough to have those charges researched by the company and removed. The card with the fraudulent charges will be canceled and a new card with a new account number will be sent to you.
On the credit card statement Figure 6.26, identify
- The balance due
- The minimum required payment
- The length of time it takes to pay off the balance by paying the minimum payments and without charging more to the card
- The interest rate for purchases
- Solution
-
- The balance due is under the payment information heading and is $3,663.23.
- The minimum payment due is also under the payment information heading, and is $36.63.
- The time to pay off the balance using only minimum payments is below the payment information, and says it takes 2 years and 4 months to pay off the balance.
- The interest rate for purchases is toward the bottom of the statement. It is 19.99%.
Referring to the statement above, answer the following:
- What is the statement period?
- What is the credit limit?
- How much in fees were charged?
- Answer
-
- From April 1, 2015, to April 30, 2015
- $9,000.00
- $5.99
Compute Interest, Balance Due, and Minimum Payment Due for a Credit Card
Computing the interest, balance due, and minimum payment depends on understanding and calculating the average daily balance on a credit card. Once that is determined, all of these values can be calculated.
Most importantly, if you pay off the entire balance each month, no interest is charged.
Average Daily Balance
Most credit card companies compute interest using the average daily balance method.
To find the average daily balance on your credit card, determine the balance on the card each day of the billing period (often that month), and take the average. One process to find the average daily balance follows these steps:
- Start with a list of transactions with their dates and amounts.
- For each day that had transactions, find the total of the transactions for the day. Expenditures are treated as positive values, payments are treated as negative values.
- Create a table containing each day with a different balance. The balance is the previous balance plus the day’s total transactions.
- Add a column for the number of days those balances until the balance changed.
- Add a column that contains the balances multiplied by the number of days until the balance changed.
- Find the sum of that last column.
- Divide the sum by the number of days in the billing period (often the number of days in the month). This is the average daily balance.
The billing cycle goes from May 1 to May 31. The balance at the start of the billing cycle is $450.21. The list of transactions on the card is below. Find the average daily balance for the credit card during the May billing period.
| Date | Activity | Amount |
|---|---|---|
| May 1 | Billing Date Balance | $450.21 |
| May 10 | Payment | $120.00 |
| May 15 | Groceries | $83.43 |
| May 26 | Auto Parts | $45.12 |
| May 26 | Restaurant | $85.34 |
| May 30 | Shoes | $98.23 |
- Solution
-
To find the average daily balance, we use the following steps.
- Start with a list of transactions with their dates and amounts.
This list is provided. - For each day that had transactions, find the total of the transactions for the day.
The only day with more than one transaction was May 26. The sum of those transactions is $130.46. Treating the payment as a negative value, the daily transaction amounts areDate Amount May 1 $450.21 May 10 \(-\)$120.00 May 15 $83.43 May 26 $130.46 May 30 $98.23 - Create a table containing each day with a different balance.
The new table with dates that had different balances is below.Date Balance May 1\(-\)9 $450.21 May 10\(-\)14 $330.21 May 15\(-\)25 $413.64 May 26\(-\)29 $544.10 May 30\(-\)31 $642.33 - Now, add a column for the number of days those balances until the balance changed. The days until the balance changes is found by finding the difference in the dates. For instance, from May 15 to May 26 was 11. Adding that column to the table, we have
The last entry was 2 since there are 31 days in May.Date Balance Number of Days Until Balance Changes May 1\(-\)9 $450.21 9 May 10\(-\)14 $330.21 5 May 15\(-\)25 $413.64 11 May 26\(-\)29 $544.10 4 May 30\(-\)31 $642.33 2 - Add a column that contains the balances multiplied by the number of days until the balance changed. We create the column and multiply the values.
Date Balance Number of Days Until Balance Changes Balance \(\times\) Number of Days May 1\(-\)9 $450.21 9 $4,051.89 May 10\(-\)14 $330.21 5 $1,651.05 May 15\(-\)25 $413.64 11 $4,550.04 May 26\(-\)29 $544.10 4 $2,176.40 May 30\(-\)31 $642.33 2 $1,284.66 Total 31 $13,714.04 - Find the sum of that last column. Adding that last column we have a sum of $13,714.04.
- There are 31 days in May, so divide the sum by 31, which gives an average of $442.39, which is the average daily balance.
- Start with a list of transactions with their dates and amounts.
The billing cycle goes from June 1 to June 30. The previous month’s balance is $563.80. The transactions are in the table below. Find the average daily balance for this credit card.
| Date | Activity | Amount |
|---|---|---|
| June 1 | Balance | $563.80 |
| June 2 | Gasoline | $47.50 |
| June 2 | Groceries | $63.42 |
| June 15 | Movie | $38.75 |
| June 15 | Payment | $250.00 |
| June 27 | Pharmacy | $31.21 |
| June 28 | Auto fuel | $48.00 |
- Answer
-
$567.32
Calculating the Interest for a Credit Card
The interest charged for a credit card is based on the daily interest rate of the card, the number of days in the billing cycle, and the average daily balance on the card.
The interest charge, \(I\), for a credit card during a billing cycle is \[I= ADB\times r \times \frac{d}{365}, \nonumber\] where \(ADB\) is the average daily balance, \(r\) is the annual percentage rate, and \(d\) is the number of days in the billing cycle. As before, interest is rounded up to the next penny.
Compute the interest charged for the credit card based on the given average daily balance (ABD), annual interest rate, and number of days in the billing cycle.
- ADB = $2,765.00, annual interest rate 13.99%, billing cycle of 30 days
- ADB = $789.30, annual interest rate 17.99%, billing cycle of 31 days
- ADB = $1,037.85, annual interest rate 11.99%, billing cycle of 28 days
- Solution
-
- Substituting $2,765.00 for ADB, 0.1399 for \(r\) and 30 for \(d\) and calculating, we find the interest charge to be \[I=\$2,765.00\times 0.1399\times\frac{30}{365} \approx \$31.80\nonumber\]
- Substituting $789.30 for ADB, 0.1799 for \(r\) and 31 for \(d\) and calculating, we find the interest charge to be \[I=\$789.30\times 0.1799\times \frac{31}{365}\approx \$12.06 \nonumber\]
- Substituting $1,037.85 for ADB, 0.1199 for \(r\) and 28 for \(d\) and calculating, we find the interest charge to be \[I=\$1,037.85 \times 0.1199 \times \frac{28}{365}\approx \$9.55\nonumber\]
Compute the interest charged for the credit card based on the given average daily balance (ABD), annual interest rate, and number of days in the billing cycle.
- ADB = $2,135.00, annual interest rate 12.9%, billing cycle of 30 days
- ADB = $1,589.63, annual interest rate 9.99%, billing cycle of 31 days
- ADB = $6,803.41, annual interest rate 14.9%, billing cycle of 28 days
- Answer
-
1. $22.64 2. $13.49 3. $77.77
The interest you pay is not the only way a credit card company generates revenue. It also charges fees to the retailers, online stores, and service providers that allow the consumer, you, to use your credit card to pay them. These are called processing fees. Currently they typically range from 2.87% to 4.35% of each transaction. That means if you use your credit card at a store and spend $100.00, the store will have to pay the credit card company somewhere between $2.87 and $4.35.
One type of processing fee is the interchange fee. Mastercard charges the vendor 1.35% of the sale, plus an additional percentage up to 3.25%, and a fixed $0.01 fee for each transaction.
Added to that is an assessment fee. This fee is 0.14% for Visa cards.
Calculating the Balance of a Credit Card
The balance, or sometimes balance due, on a credit card is the previous balance, plus all expenses, minus all payments and credits, plus the interest on the card. As stated before, if the card was paid off, there is no interest to be paid.
Kaylen’s credit card charges 16.9% annual interest. His current billing period is from November 1 to November 30. The balance on November 1 was $1,845.23. Use Kaylen’s following transactions to determine his balance due at the end of the billing cycle.
| Date | Activity | Amount |
|---|---|---|
| November 1 | Billing Date Balance | $1,845.23 |
| November 3 | Groceries | $78.50 |
| November 4 | Tablet | $159.00 |
| November 4 | Online Game Purchase | $39.99 |
| November 4 | Restaurant | $47.10 |
| November 10 | Payment | $300.00 |
| November 10 | Gasoline | $58.75 |
| November 13 | Clothing | $135.00 |
| November 18 | Gift | $30.00 |
| November 18 | Restaurant | $21.75 |
| November 28 | Gasoline | $43.79 |
- Solution
-
The first step is to find Kaylen’s average daily balance. To find the average daily balance, we use the following steps.
- Start with a list of transactions with their dates and amounts.
This list is provided. - For each day that had transactions, find the total of the transactions for the day. The days with more than one transaction were Nov. 4, Nov. 13, and Nov. 18. Treating the payment on November 10 as a negative value, the daily transaction amounts are
Date Amount November 1 $1,845.23 November 3 $78.50 November 4 $246.09 November 10 \(-\)$300.00 November 13 $193.75 November 18 $51.75 November 28 $43.79 - Create a table containing each day with a different balance. The new table with dates that had different balances is below.
Date Balance November 1\(-\)2 $1,845.23 November 3 $1,923.73 November 4\(-\)9 $2,169.82 November 10\(-\)12 $1,869.82 November 13\(-\)17 $2,063.57 November 18\(-\)27 $2,115.32 November 28\(-\)30 $2,159.11 - Now, add a column for the number of days those balances until the balance changed. The days until the balance changes is found by finding the difference in the dates. For instance, from May 15 to May 26 was 11. Adding that column to the table we have
The last entry was 3 since there are 30 days in November (the 28th, 29th, and 30th).Date Balance Number of Days Until Balance Changes November 1\(-\)2 $1,845.23 2 November 3 $1,923.73 1 November 4\(-\)9 $2,169.82 6 November 10\(-\)12 $1,869.82 3 November 13\(-\)17 $2,063.57 5 November 18\(-\)27 $2,115.32 10 November 28\(-\)30 $2,159.11 3 - Add a column that contains the balances multiplied by the number of days until the balance changed. We create the column and multiply the values.
Date Balance Number of Days Until Balance Changes Balance \(\times\) Number of Days November 1\(-\)2 $1,845.23 2 $3,690.46 November 3 $1,923.73 1 $1,923.73 November 4\(-\)9 $2,169.82 6 $13,018.92 November 10\(-\)12 $1,869.82 3 $5,609.46 November 13\(-\)17 $2,063.57 5 $10,317.85 November 18\(-\)27 $2,115.32 10 $21,153.20 November 28\(-\)30 $2,159.11 3 $6,477.33 Total 30 $62,190.95 - Find the sum of that last column. Adding that last column we have a sum of $62,190.95.
- There are 30 days in November, so divide the sum by 30, which gives an average of $2,073.03, which is the average daily balance.
With the average daily balance, we can determine the interest that is charged for November. Substituting ADB = $2,073.03, = 0.169, and = 30 into the formula and calculating, \[ I=ABD\times r\times \frac{d}{365} = \$2,073.03 \times 0.169 \times \frac{30}{365} \approx \$28.80\nonumber\]
we find the interest to be
$ 28.80 - Start with a list of transactions with their dates and amounts.
Angel’s credit card charges 16.9% annual interest. His current billing period is from August 1 to August 31. The balance on August 1 was $982.45. Use Angel’s following transactions to determine his balance due at the end of the billing cycle.
| Date | Activity | Amount |
|---|---|---|
| August 1 | Billing Date Balance | $982.45 |
| August 5 | Food | $125.31 |
| August 13 | Payment | $500.00 |
| August 14 | Gasoline | $51.65 |
| August 14 | Pizza | $36.99 |
| August 14 | Shoes | $89.45 |
| August 19 | Electric bill | $178.34 |
| August 21 | Internet | $36.99 |
| August 21 | Food | $93.45 |
| August 30 | Gasoline | $43.18 |
- Answer
-
$1,152.35
Minimum Payment Due
The minimum payment due is the smallest required amount that must be paid on a credit card to avoid late fees and penalties, such as an increased interest rate. The calculation of this amount may vary from card to card and also depends on the balance of the credit card.
General guidelines for determining the minimum payment due are:
- For larger balances (usually over $1,000), the minimum payment is typically a percentage of the balance.
- For moderate balances (between $25 and $1,000), the minimum is often a specified dollar amount—$25 is a common figure.
- If the balance is small (under $25, for instance), then the minimum payment is the full balance.
These are just general guidelines; the exact terms can vary depending on the credit card issuer.
Minimum payments should only be made when money is tight in a given month. Paying only the minimum extends the time it takes to pay off the balance and results in significant interest charges. This practice is strongly discouraged.
Check Your Understanding
- Name three important pieces of information that are included in a credit card statement.
- A credit card has an average daily balance of $1,428.50 during a 31-day billing cycle. Find the interest charge if the annual interest rate is 15.9%.
- The billing cycle goes from June 15 to July 14, or 30 days. The balance at the start of the billing cycle is $3,825.50. The list of transactions on the card is below. Find the average daily balance.
| Date | Activity | Amount |
|---|---|---|
| June 15 | Billing Date Balance | $3,825.50 |
| June 20 | Food | $125.31 |
| June 20 | Clothing | $345.00 |
| June 29 | Payment | $750.00 |
| July 1 | Restaurant | $94.80 |
| July 6 | Gasoline | $49.75 |
| July 6 | Home Repair Supplies | $683.94 |
| July 6 | Internet | $49.99 |
| July 10 | Cell Phone | $85.00 |
| July 10 | Food | $175.24 |
4. Find the balance due on a credit card statement if ADB = $487.65, the annual interest rate is 16.8%, the billing cycle was 30 days, and the balance at the end of the billing cycle, before interest is added, was $689.47.
- Display Answers
-
- Due date, minimum payment due, and balance due
- $19.30
- $4,104.27
- $696.21
Exercises
1. How much interest does a credit card holder pay if they pay off the balance every month?
2. Use the credit card statement below to answer the following questions.
- (a) What is the minimum payment due?
- (b) How long will it take to pay the balance if the minimum only is paid and no new purchases are made?
- (c) How much interest was charged in this billing cycle?
- (d) What is the balance on the credit card?
- (e) What is the credit limit on this card?
- (f) What is the late payment fee for this card?
- (g) When is the payment due?
3. The billing cycle for a credit card goes from April 1 to April 30. The balance at the start of the billing cycle is $1,598.00. The list of transactions on the card is below.
- (a) Find the average daily balance for the billing cycle.
- (b) If the credit card charges 11.9% annual interest, determine the balance due at the end of the billing cycle.
| Date | Activity | Amount |
|---|---|---|
| April 1 | Billing Date Balance | $1,598.00 |
| April 9 | Gasoline | $51.24 |
| April 9 | Food | $105.56 |
| April 9 | Payment | $675.00 |
| April 13 | Camping Trip | $229.75 |
| April 21 | Gasoline | $38.45 |
| April 22 | Gifts | $148.88 |
| April 22 | Food | $49.75 |
| April 30 | Gym Payment | $74.99 |
4. The billing cycle for a credit card goes from September 1 to September 30. The balance at the start of the billing cycle is $384.25. The list of transactions on the card is below.
- (a) Find the average daily balance for the billing cycle.
- (b) If the credit card charges 8.9% annual interest, determine the balance due at the end of the billing cycle.
| Date | Activity | Amount |
|---|---|---|
| September 1 | Billing Date Balance | $384.25 |
| September 2 | Food | $94.54 |
| September 5 | Gasoline | $25.65 |
| September 5 | Internet | $39.99 |
| September 6 | Payment | $380.00 |
| September 9 | Insurance | $174.52 |
| September 16 | Food | $83.54 |
| September 16 | Day Care | $350.00 |
| September 20 | Tires | $2,337.56 |
| September 21 | Child Clothing | $27.65 |
| September 21 | Gasoline | $31.00 |
| September 28 | Television | $299.95 |
5. The billing cycle for a credit card goes from October 10 to November 9. The balance at the start of the billing cycle is $930.50. The list of transactions on the card is below.
- (a) Find the average daily balance for the billing cycle.
- (b) if the credit card charges 18.9% annual interest, determine the balance due at the end of the billing cycle.
| Date | Activity | Amount |
|---|---|---|
| October 10 | Billing Date Balance | $930.50 |
| October 11 | Clothing | $350.00 |
| October 14 | Computer | $865.84 |
| October 17 | Food | $106.51 |
| October 21 | Payment | $700.00 |
| October 21 | Restaurant | $134.52 |
| October 21 | Hotel | $387.56 |
| October 30 | Hockey Game | $76.47 |
| November 5 | Memorabilia | $150.00 |
| November 5 | Restaurant | $94.45 |
| November 6 | Gasoline | $49.19 |
6. The billing cycle for a credit card goes from February 15 to March 16 during a non-leap year. The balance at the start of the billing cycle is $292.82. The list of transactions on the card is below.
- (a) Find the average daily balance for the billing cycle.
- (b) If the credit card charges 10.9% annual interest, determine the balance due at the end of the billing cycle.
| Date | Activity | Amount |
|---|---|---|
| February 15 | Billing Date Balance | $292.82 |
| February 21 | Food | $64.57 |
| February 22 | Gasoline | $31.50 |
| February 22 | Food | $71.94 |
| February 28 | Insurance | $133.25 |
| February 28 | Payment | $100.00 |
| March 3 | Gasoline | $26.61 |
| March 12 | School Trip | $300.00 |
7. In the following exercises, compute the interest charged for the credit card based on the given average daily balance (ABD), annual interest rate, and number of days in the billing cycle.
- (a) ADB = $350.00, annual interest rate 14.9%, billing cycle of 30 days.
- (b) ADB = $4,312.00, annual interest rate 9.99%, billing cycle of 31 days.
- (c) ADB = $563.38, annual interest rate 17.9%, billing cycle of 30 days.
- (d) ADB = $1,043.53, annual interest rate 11.9%, billing cycle of 31 days.
8. The billing cycle for a credit card goes from March 15 to April 14. The balance at the start of the billing cycle is $450.00. The list of transactions on the card is below.
- (a) Find the average daily balance for the billing cycle.
- (b) If the annual interest rate is 15.9%, what is the balance due at the end of the billing cycle?
| Date | Activity | Amount |
|---|---|---|
| March 15 | Billing Date Balance | $450.00 |
| March 21 | Movie | $50.00 |
| March 28 | Gasoline | $65.00 |
| March 31 | Snacks | $15.50 |
| April 1 | Dinner | $63.60 |
| April 1 | Payment | $300.00 |
| April 1 | Gasoline | $48.90 |
| April 9 | Plane Tickets | $288.50 |
9. The average daily balance for Greg’s last credit card statement was $1,403.50. The card charges 15.9% interest. If the billing cycle for that statement was 30 days, how much interest is Greg charged?
10. The billing cycle for Therese’s credit card is from July 7 to August 6 (31 days). The interest rate on the card is 17.9%. The balance at the start of the billing cycle is $925.00. The table below lists her transactions during the cycle. What is her balance due at the end of the billing cycle?
| Date | Activity | Amount |
|---|---|---|
| July 7 | Billing Date Balance | $925.00 |
| July 10 | Child Care | $850.00 |
| July 10 | Gasoline | $51.00 |
| July 12 | Food | $135.50 |
| July 18 | Payment | $750.00 |
| July 18 | Pizza | $35.00 |
| July 18 | Gift | $25.00 |
| July 21 | Food | $121.75 |
| July 30 | Gasoline | $47.50 |
| August 1 | Department store | $173.00 |
| August 4 | Food | $98.00 |