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Credit Cards

Apply for a credit card armed with basic knowledge.

Learning Objectives

After completing this section, you should be able to:

Apply for a credit card armed with basic knowledge.
Distinguish between three basic types of credit cards.
Compare and contrast the benefits and drawbacks of credit cards.
Read and understand the basic parts of a credit card statement.
Compute interest, balance due, and minimum payment due for a credit card.

Types of Credit Cards

There are basically three types of credit cards: bank-issued credit cards, store-issued credit cards, and travel/entertainment credit cards. We will look at all three and explain the good and the bad qualities of each.

Bank-Issued Credit Cards

Perhaps the most widely used credit card type is the bank-issued credit card, like Visa or MasterCard (and even American Express and Discover cards). These types of cards are an example of revolving credit, meaning that additional credit is extended before the previous balance is paid—but only up to the assigned credit limit. Bank-issued cards are considered the most convenient, as they can be used to purchase anything, including apparel, furniture, groceries, fuel for automobiles, meals, hotel bills, and so on, just as if paying with cash. The interest rates on bank-issued credit cards are usually lower than those for other credit cards we’ll discuss, and the credit limits are generally higher. Currently, bank-issued cards have an average 20.09% APR.

Store-Issued Credit Cards

Store-issued credit cards are issued by retailers. One can hardly walk into a store these days without being offered a discount on purchases if one applies for the store credit card. These cards can only be used in that store or family of stores that issues the card. However, if a store credit card is associated with Visa, MasterCard, or American Express, then the card might be used the same way that the bank-issued cards are used. This is called cobranding. The logo of the bank-issued card will be present on the store card. Many stores offer both types. Like other credit cards, they may come with an annual fee.

Store credit cards usually charge higher interest rates than bank-issued cards. Currently, store credit cards have an APR (annual percentage rate) of 24.15%. Any rewards offered by store credit cards are usually limited to purchases made in their own store, and it typically takes longer to accumulate enough rewards or points to redeem them, whereas cobranded credit cards offer opportunities to earn rewards on all purchases, regardless of whether purchases are made in the issuing store or not.

Store credit cards usually offer lower credit limits, at least in the beginning. After being proved to be a responsible credit card owner, credit limits can be raised. Nevertheless, store credit cards are a good choice for those new to the credit card industry. If on-time payments are consistently made, it is an excellent way to get started building a credit history.

Travel/Entertainment Cards, or Charge Cards

This is the third type of credit card. The travel and entertainment cards, also known as charge cards, first and foremost offer very high limits or unlimited credit, but they must be paid in full every month. They generally charge high annual fees and impose expensive penalties should a payment be late. On the other hand, they typically have longer grace periods and offer many and various kinds of rewards.

Check out this nerdwallet article about the differences between a charge card and a credit card.

Top Travel and Entertainment Cards

At one time, Diner’s Club was the premier entertainment card. To be accepted into the Diner’s Club and be rewarded with a charge card meant one was special. Today, an American Express card is held with the same reverence as Diner’s Club was in the past. It was a privilege to own one of these cards. There is a lot of competition going on to supplant Diner’s Club, as shown by the Chase Sapphire Preferred Card’s travel rewards and benefits.

Another thing worth mentioning here and something that appears to be an unusual offering is part of the American Express Gold and higher-level cards. Cardholders can actually open a savings account, buy a CD, or apply for a personal or business loan from American Express. The company boasts a higher interest rate than what is paid on traditional savings accounts and CDs.

Comparing Credit Cards

Try it.

Which type of credit card is paid off every month so has no interest to be paid, but comes with high fees?
Which type of credit cards are the most widely accepted?
Which type of credit cards are the most limited?

Solution

Charge cards are to be paid off completely each month.
Bank-issued credit cards are the most flexible to use, because they are not limited to which retailers or service providers accept them.
Store issues credit cards are the most limited, since they only work in that family of stores.

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, 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. 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.

Reading a Credit Card Statement

Try it.

On the credit card statement , 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%.

Compute Interest, Balance Due, and Minimum Payment Due for a Credit Card

Computing all of these values depends on understanding and computing the average daily balance on a credit card. Once that is known, the interest, balance due, and minimum payment can be found.

Above all else, if you pay off the entire balance each month, interest is not 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 that 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.

Condensed — the full section is in OpenStax Contemporary Mathematics.

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.

Calculating Interest for a Credit Card Billing Cycle

Try it.

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 $I=\frac{\text{ADB}\times r\times d}{365}=\frac{\text{\$}2,765.00\times 0.1399\times 30}{365}=\text{\$}31.80$.
Substituting $789.30 for ADB, 0.1799 for $r$ and 31 for $d$ and calculating, we find the interest charge to be $I=\frac{\text{ADB}\times r\times d}{365}=\frac{\text{\$}789.30\times 0.1799\times 31}{365}=\text{\$}12.06$.
Substituting $1,037.85 for ADB, 0.1199 for $r$ and 28 for $d$ and calculating, we find the interest charge to be $I=\frac{\text{ADB}\times r\times d}{365}=\frac{\text{\$}1,037.85\times 0.1199\times 28}{365}=\text{\$}9.55$.

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.

Calculating the Balance of a Credit Card

Try it.

Find the balance on the credit card with the given interest charge and balance before interest was charged. The cards were not paid off previously.

Balance before interest is $708.50, interest charge is $8.15
Balance before interest is $1,395.10, interest charge is $21.32

Solution

Adding the balance before interest to the interest charge, we find the balance to be $716.65.
Adding the balance before interest to the interest charge, we find the balance to be $1,416.42.

The next example puts all those steps together.

Condensed — the full section is in OpenStax Contemporary Mathematics.

Minimum Payment Due

The minimum payment due is the smallest required amount to be paid on a credit card to avoid late fees and penalties, such as an increased interest rate. The calculations for this may differ from card to card. They also depend in the balance of the credit card. General guidelines for minimum payment due are:

For larger balances (usually over $1,000), the minimum payment will be some percentage of the balance due.
For moderate balances (between $25 and $1,000), the minimum would be a specified dollar amount. $25 seems to be a common value.
If the balance is small (under $25 for instance), then the minimum payment is the balance.

Those are just guidelines. Individual cards may vary in these values.

Minimum payments should only be paid if money is short in a given month. The length of time to pay off a credit card using minimum payments is quite long, and results in paying a lot of interest. It is strongly discouraged.

Calculate the Minimum Payment Due

Try it.

The FYA credit card company has the following minimum payment policy. For balances over $1,000, the minimum payment is 2.5% of the balance due plus fees, but not interest. For balances between $500.00 and $999.99, the minimum payment is $50.00. For balances $499.99 and under, the minimum payment is $25.00 or the balance due, whichever is smaller.

In the following, calculate the minimum payment due given the credit card minimum payment policy, the balance due and fees charged.

Balance due is $1,309.00, no fees
Balance due is $265.50, $35 in fees
Balance due is $784.90, no fees

Solution

The balance is over $1,000, so the minimum payment is 2.5% of the balance due plus fees. 2.5% of the balance due is $0.025\times \text{\$}1,309.00=\text{\$}32.73$. Since there are no fees, the minimum payment due is $32.73.
The balance is under $499.99, so the minimum payment due is $25.00.
The balance is between $500.00 and $999.00, so the minimum payment due is $50.00.

Check out this nerdwallet article about minimum payments for more!

Key Concepts

Credit cards can be a flexible way to pay for almost anything, but can become a financial hazard if used unwisely.
When deciding which credit card to apply for, evaluate the interest rate, fees (annual and late), reward programs and credit limit. Be sure they meet your criteria.
Paying off the balance of your credit card every month will control your spending and will never result in paying interest.
Credit card statements hold all important information about your credit card, including payment, balances, charges and billing cycle dates.
Although the minimum payment is attractive precisely because it is so small, paying only the minimum results is a long payoff term and higher interest costs.

Practice (7)

Try each one on paper first. Reveal the answer to check; verified ones can be opened in the solver for every step.

1. Which type of credit card is paid off every month so has no interest to be paid, but comes with high fees?
2. Which type of credit cards are the most widely accepted?
3. Which type of credit cards are the most limited?
Revelează răspunsul
1. Charge cards are to be paid off completely each month.
2. Bank-issued credit cards are the most flexible to use, because they are not limited to which retailers or service providers accept them.
3. Store issues credit cards are the most limited, since they only work in that family of stores.
On the credit card statement , identify
1. The balance due
2. The minimum required payment
3. The length of time it takes to pay off the balance by paying the minimum payments and without charging more to the card
4. The interest rate for purchases
Revelează răspunsul
1. The balance due is under the payment information heading and is $3,663.23.
2. The minimum payment due is also under the payment information heading, and is $36.63.
3. 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.
4. The interest rate for purchases is toward the bottom of the statement. It is 19.99%.
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.
Date Activity Amount
1-May Billing Date Balance $450.21
10-May Payment $120.00
15-May Groceries $83.43
26-May Auto Parts $45.12
26-May Restaurant $85.34
30-May Shoes $98.23
Find the average daily balance for the credit card during the month of May.
Revelează răspunsul
To find the average daily balance, we use the following steps.
1. Start with a list of transactions with their dates and amounts.
  This list is provided.
2. 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 are
  
  Date Amount
  1-May $450.21
  10-May -$120.00
  15-May $83.43
  26-May $130.46
  30-May $98.23
3. Create a table containing each day with a different balance.
  The new table with dates that had different balances is below.
  
  Date Balance
  1-May $450.21
  10-May $330.21
  15-May $413.64
  26-May $544.10
  30-May $642.33
4. 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
  
  Date Balance Days Until Balance Changes
  1-May $450.21 9
  10-May $330.21 5
  15-May $413.64 11
  26-May $544.10 4
  30-May $642.33 2
  The last entry was 2 since there are 31 days in May.
5. 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 Days Until Balance Changes Balance Times Days
  1-May $450.21 9 $4,051.89
  10-May $330.21 5 $1,651.05
  15-May $413.64 11 $4,550.04
  26-May $544.10 4 $2,176.40
  30-May $642.33 2 $1,284.66
6. Find the sum of that last column. Adding that last column we have a sum of $13,714.04.
7. 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.
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.
1. ADB = $2,765.00, annual interest rate 13.99%, billing cycle of 30 days
2. ADB = $789.30, annual interest rate 17.99%, billing cycle of 31 days
3. ADB = $1,037.85, annual interest rate 11.99%, billing cycle of 28 days
Revelează răspunsul
1. Substituting $2,765.00 for ADB, 0.1399 for $r$ and 30 for $d$ and calculating, we find the interest charge to be $I=\frac{\text{ADB}\times r\times d}{365}=\frac{\text{\$}2,765.00\times 0.1399\times 30}{365}=\text{\$}31.80$.
2. Substituting $789.30 for ADB, 0.1799 for $r$ and 31 for $d$ and calculating, we find the interest charge to be $I=\frac{\text{ADB}\times r\times d}{365}=\frac{\text{\$}789.30\times 0.1799\times 31}{365}=\text{\$}12.06$.
3. Substituting $1,037.85 for ADB, 0.1199 for $r$ and 28 for $d$ and calculating, we find the interest charge to be $I=\frac{\text{ADB}\times r\times d}{365}=\frac{\text{\$}1,037.85\times 0.1199\times 28}{365}=\text{\$}9.55$.
Find the balance on the credit card with the given interest charge and balance before interest was charged. The cards were not paid off previously.
1. Balance before interest is $708.50, interest charge is $8.15
2. Balance before interest is $1,395.10, interest charge is $21.32
Revelează răspunsul
1. Adding the balance before interest to the interest charge, we find the balance to be $716.65.
2. Adding the balance before interest to the interest charge, we find the balance to be $1,416.42.

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
1-Nov	Billing Date Balance	$1,845.23
3-Nov	Groceries	$78.50
4-Nov	Tablet	$159.00
4-Nov	Online Game Purchase	$39.99
4-Nov	Restaurant	$47.10
10-Nov	Payment	$300.00
13-Nov	Gasoline	$58.75
13-Nov	Clothing	$135.00
18-Nov	Gift	$30.00
18-Nov	Restaurant	$21.75
28-Nov	Gasoline	$43.79

Revelează răspunsul

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
1-Nov $1,845.23
3-Nov $78.50
4-Nov $246.09
10-Nov -$300.00
13-Nov $193.75
18-Nov $51.75
28-Nov $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
1-Nov $1,845.23
3-Nov $1,923.73
4-Nov $2,169.82
10-Nov $1,869.82
13-Nov $2,063.57
18-Nov $2,115.32
28-Nov $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 Days Until Balance Changes
1-Nov $1,845.23 2
3-Nov $1,923.73 1
4-Nov $2,169.82 6
10-Nov $1,869.82 3
13-Nov $2,063.57 5
18-Nov $2,115.32 10
28-Nov $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	Days Until Balance Changes	Balance Times Days
1-Nov	$1,845.23	2	$3,690.46
3-Nov	$1,923.73	1	$1,923.73
4-Nov	$2,169.82	6	$13,018.92
10-Nov	$1,869.82	3	$5,609.46
13-Nov	$2,063.57	5	$10,317.85
18-Nov	$2,115.32	10	$21,153.20
28-Nov	$2,159.11	3	$6,477.33

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, $r$ = 0.169, and $d$ = 30 into the formula $I=\frac{\text{ADB}\times r\times d}{365}$ and calculating, we find the interest to be $I=\frac{\text{ADB}\times r\times d}{365}=\frac{\text{\$}2,073.03\times 0.169\times 30}{365}=\text{\$}28.80$.
This interest is added to the final balance from the table in step 3, $2,159.11, which yields a balance due of $2,101.83.

The FYA credit card company has the following minimum payment policy. For balances over $1,000, the minimum payment is 2.5% of the balance due plus fees, but not interest. For balances between $500.00 and $999.99, the minimum payment is $50.00. For balances $499.99 and under, the minimum payment is $25.00 or the balance due, whichever is smaller.
In the following, calculate the minimum payment due given the credit card minimum payment policy, the balance due and fees charged.
1. Balance due is $1,309.00, no fees
2. Balance due is $265.50, $35 in fees
3. Balance due is $784.90, no fees
Revelează răspunsul
1. The balance is over $1,000, so the minimum payment is 2.5% of the balance due plus fees. 2.5% of the balance due is $0.025\times \text{\$}1,309.00=\text{\$}32.73$. Since there are no fees, the minimum payment due is $32.73.
2. The balance is under $499.99, so the minimum payment due is $25.00.
3. The balance is between $500.00 and $999.00, so the minimum payment due is $50.00.

Symbols used here

\pm

plus or minus
Both signs at once: x = 3 ± 2 means 5 and 1.

\neq

not equal
The two sides are different.

\leq,\ \geq

less/greater than or equal
Inequalities that allow equality; < and > exclude it.

\approx

approximately equal
Equal to the precision shown, not exactly.

\sqrt{x},\ \sqrt[n]{x}

square root, n-th root
The non-negative number whose square (n-th power) is x.

a \bmod n

remainder
What is left after dividing a by n.

per cent
Per hundred: 15% = 15/100.

a : b,\ \frac{a}{b}

ratio, fraction
a for every b; a divided by b.

How to: Credit Cards

Apply for a credit card armed with basic knowledge.
Distinguish between three basic types of credit cards.
Compare and contrast the benefits and drawbacks of credit cards.
Read and understand the basic parts of a credit card statement.
Compute interest, balance due, and minimum payment due for a credit card.
Which type of credit card is paid off every month so has no interest to be paid, but comes with high fees?
Which type of credit cards are the most widely accepted?
Which type of credit cards are the most limited?

Questions people ask

Why does the order of operations matter?

Because 2 + 3 × 4 would otherwise be two different numbers. The convention (brackets, exponents, multiplication and division, addition and subtraction) exists so every reader gets the same value from the same expression.

How do I check an arithmetic answer?

Estimate first (round every number and compute roughly), then compare. If the estimate and the exact answer disagree by more than a little, one of them is wrong. The solver shows every operation, so you can find which line went astray.

Why are fractions harder than decimals?

They are not harder, they are more exact: 1/3 is a precise number, 0.333 is an approximation. Fractions need a common denominator to add, which is the one extra step people trip on.

Încearcă pe tine.

Parts of this page are adapted from OpenStax Contemporary Mathematics (CC BY-NC-SA 4.0). Condensed and re-explained here; errors are ours.

Mai multe în Arithmetic

Order of operations Fractions Percentages Powers and roots

Date	Amount
1-May	$450.21
10-May	-$120.00
15-May	$83.43
26-May	$130.46
30-May	$98.23