Credit cards are well-known for their utility to both businesses and individual consumers. It’s also no secret that allowing credit card debt to get out of control can be terrible for your financial health. Given these realities, a strong understanding of the mathematics involved in their application is both worthwhile and essential.

**What is a credit card?**

Credit cards are a convenient and flexible way to use a bank’s credit capacity to pay for products (borrowed money). Swiping your credit card through the payment machine at the gas/petrol pump may not appear to be a loan, but you are borrowing each time you make a transaction. The bank (or other financial organization) that issued your card pays the gas station on your behalf, and you refund the bank later.

The financial institution is the lender, and you are the borrower. People use credit cards to purchase products for which they do not have the cash to pay in full. More than the obligation to borrow money to pay, there are various other reasons to use a credit card to pay for anything. At the gas station or shopping mall, you may be able to pay with cash, but you prefer to use a credit card because it is easier to pay at the pump. Using a credit card to pay for online purchases is usually significantly more convenient than using alternative methods.

Furthermore, using a credit card to pay for some purchases (such as hotel rooms and automobile rentals) may obviate the need to leave a large deposit. Some card issuers provide “cash back” or frequent flyer mile bonuses as additional reasons to use a credit card. Using a credit card, regardless of your intentions, entails borrowing money, whether you plan to do so or not.

Because using a credit card necessitates borrowing funds, it also necessitates the payment of interest. One common critique of credit cards is that their interest rates can be rather high when compared to other types of loans, such as a car or home loans. Car or housing loans, on the other hand, are secured loans. This means that if you don’t pay back the loan on time, the lender has the authority/right to seize the property you borrowed money for.

The vehicle serves as collateral for a vehicle loan, while the house serves as collateral for a mortgage or home equity loan. Secured loans are those that have a piece of collateral attached to them. Lenders would prefer that you repay the loan, but if you don’t, they may at least claim the collateral to collect the money you owe them. On the other hand, credit cards are often unsecured loans. A credit card is typically issued without any form of security. The only assurance the lender has is that you will repay the loan.

If you don’t pay back what you owe, the lender can—and will—take legal action to recover the money, but it doesn’t have the authority to confiscate any of your personal property as compensation. Credit card debts are frequently resolved in bankruptcy court, where the lender is usually only able to collect a portion of what is due. Credit card interest rates are higher in order for the lender to make up for these types of losses. This also means that candidates for credit cards with good credit histories may be able to acquire a card with a reduced interest rate because the danger of them defaulting is lower.

**Calculation of Interest and Average Daily Balance**

It may be tough to calculate credit card interest. On the one hand, because monthly statements are created and payments are due, it is reasonable to compute and charge interest to the account on a monthly basis. Because the balance fluctuates from day to day, it appears that interest should be calculated daily to account for the fact that the principal owing does not remain constant during the month.

Assume I owe an Rs500 debt on my credit card at the beginning of April. On April 5, I charge Rs300, make an Rs200 payment on April 14, and charge Rs1,600 on April 30.

If we’re going to calculate my interest monthly, what should we use as the principal? At the end of the month, the total money was Rs2,200 (500+300-200+1,600). But charging a month’s interest on Rs2,200 doesn’t seem fair, especially because my balance was much lower until one day near the end of the month. The initial sum was Rs500 but keeping it as the principle would ignore the greater balances that grew throughout the month.

There are various methods for computing interest on a credit card, but the average daily balance (ADB) method is the most prevalent. The ADB technique is used to compute and apply interest to the account monthly, and the question of principal is answered by charging interest on the average of the daily amounts for the month. This seems like a reasonable solution to the problem of shifting balances.

**Calculation of Credit Card Average Daily Balances**

*ADB = Total of (Balance x Days) Column / Total of Days OS balance Column*

*ADB = Rs21,000/30 = Rs700*

**Calculating Credit Card Interest**

Calculating credit card interest is simple once we’ve computed the ADB. We can use the basic interest formula with the ADB as the principal because there is no compounding during the billing month. The passage of time is one potential stumbling obstacle. T can be thought of as a month (i.e. T = 1/12) or as the number of days in a billing period (i.e. T = (number of days in the billing period)/ (number of days in the year). In most situations, the interest with time is computed by dividing the number of days in the billing period by the number of days in the billing period. The simple formula to calculate interest is,

**I = PRT**

Where **I **stand for Interest (in terms of Rupees)

**P** is the total principal amount i.e., ADB

**R **is the rate in annual interest percent

**T** is time amount O/S during the month (i.e., Total # of Days O/S balance)

Suppose that Jamila’s credit card in this example carries an interest rate of 16%. How much interest would she owe for the billing month from the above example?

I = 700 x .16 x 30/365 = So her interest for this billing month would be Rs 9.21

Interest will be added to her balance at the end of this billing period; the total balance on her August 17 statement will be Rs2,200+ Rs 9.21= Rs2,209.21.

**Credit Card Interest and the Grace Period**

Most credit cards include a grace period, which adds a distinct dimension to the interest issue. The grace period is a period of time that begins on the card’s billing date and normally lasts 20 to 25 days. If you pay off your previous month’s payment in full and pay off your total obligation within the grace period, you will not be charged interest (such that none of your balance is a carryover from the previous month). For individuals who only use their credit card for convenience, this can save a lot of money. Many people have credit cards that they use every day but never pay interest on. The term “convenience users” is employed. The grace period is one of the few “free lunches” in the financial world; charges on the card become a short-term interest-free loan. A convenience user benefits from the ease of using his/her credit card as well as the free temporary usage of someone else’s money. Grace periods, on the other hand, are all-or-nothing; the grace period will only apply if the amount is paid in full. Even if you pay a penny less than the whole sum, interest will still be charged.

**Example**

For example, Nomi’s credit card payment is due on the 18th of every month. His credit card has a 20-day grace period and a 21.99 percent interest rate. On October 18, his account balance was Rs935.14. He charged Rs56.65 on October 20, Rs309.25 on October 29, Rs81.17 on November 9, and Rs101.42 on November 17. He paid Rs935.14 on November 3rd. If he settles the amount on his November 18 statement in full before the grace period ends, how much interest would he owe?

Since he paid his October 18 balance in full within the grace period (which he was required to pay on or before November 6). Whereas, if he pays the November balance in full on or before the due date plus the applicable grace period, he will owe no interest.

**Other Credit Card Fees and Expenses**

Interest is perhaps the most important source of profit for credit card issuers, but it is not the only means for the issuer to make money. Annual fees and commissions are two more.

**An annual fee** is

a charge that the cardholder pays just for the privilege of having the credit card. Annual fees can be as high as Rs14,000 per year (or even more) but are usually much lower.

**Commissions** are

not paid by the cardholder, and in fact many credit card users are not even aware of their existence. When a merchant accepts a payment by a credit card, the merchant pays a fee to the credit card company. Commissions apply to debit card transactions as well. These commissions may be a percent of the amount charged, a flat amount per transaction, or a combination of the two.

**Example of Commissions**

Tanveer bought a pair of shoes for Rs17,248 and charged them to his credit card. The credit card company charges the shoe store Rs72 for each transaction, plus 1.25% of the amount charged. How much will the credit card company pay to the shoe store? The percent portion of the commission would be: (0.0125) (Rs17,248) = Rs215.6. To this, we add the Rs72 charge to arrive at a total commission of Rs215.6+ Rs72= Rs287.6. Subtracting this from the amount of the charge, we can determine that the shoe store will receive Rs17,248 – Rs287.6= Rs16,960.4.

These commissions may be insignificant to you as a customer, but they may be a big concern for businesses. Of course, the shoe retailer would like to avoid paying the Rs287.6 to the credit card company and instead, receive the full Rs17,248 for Travis’s shoes.

**Choosing the Best Deal**

The credit card market is fiercely competitive, with hundreds of different card issuers competing for each potential card customer. Many customers will just accept whichever credit card offer appears to be the most convenient, yet cards come with a broad variety of interest rates and fees. People who simply accept the first offer that comes their way sometimes ignore or lose out on the possibility of spending less on their credit card use.

As a customer, you should ideally select the card with the lowest interest rate and the lowest annual fee. No computations are required if one of your alternatives has the lowest cost for both of them. The decision is self-evident. But what if the card with the lowest annual charge has a higher interest rate, and the card with the lowest interest rate has a high annual cost? How can we compare the interest rate to the yearly charge to see which is the better deal?

Assume you have the option of getting a Visa card from one of three different banks. The offers made by the banks are listed in the table below. (Note that the acronym APR, short for annual percentage rate, is used in this table; it is standard practice on credit card offers to identify the interest rate in this manner.)

**Card Issuer APR Annual Fee**

Bank A 9% Rs80

Bank B 15% Rs25

Bank C 23.99% None

Which offer is the best? The answer is entirely dependent on how you intend to utilize the card. The interest rate is unimportant if you are a convenience user who pays your account during the grace period each month. You’re not going to pay any interest anyhow, so the interest rate makes no difference to you. In such a situation, Bank C is your best option because there is no annual charge, and you may use this card for free. On the other hand, for someone with a substantial amount, the savings from a low-interest rate would more than offset a hefty yearly charge, making Bank A the clear winner. The decision is more difficult for someone in the middle, who may have a balance but not one substantial enough to offset a higher yearly charge with a reduced interest rate. In this situation, we must first estimate how much of a balance will be carried before computing the figures.

The example below will demonstrate how to choose the best price,

Jaffar anticipates carrying a credit card amount of about Rs800 on a regular basis. Which of the three alternatives shown in the table above would be the cheapest for him?

The entire annual cost of each card may be calculated. Given that he will be carrying a balance of about Rs800, his annual interest costs at Bank A will be:

For Bank B, the interest would be ** I = PRT** = (Rs800) (0.09) (1) = Rs72. Added to the Rs80 annual fee would total Rs152

For Bank B, the interest would be ** I = PRT** = (Rs800) (0.15) (1) = Rs120. Added to the Rs25 annual fee would total Rs145

For Bank B, the interest would be ** I = PRT** = (Rs800) (0.2399) (1) = Rs191.92. Added to the Rs0 the annual fee would total Rs191.92

In Jaffar’s instance, it’s definitely worth paying an annual fee and choosing Bank A or B. The overall cost of Bank B is the lowest. However, if Jaffar has other reasons to favor Bank A (convenience, existing banking relationship, etc.), he may select that choice, given the difference is only a few dollars and is simply an estimate anyhow. Bank B, on the other hand, has the lowest anticipated cost and, absent any other considerations, is the best option.

Jaffar’s expected balance of Rs800 is big enough to justify foregoing Bank C’s no-annual-cost offer in favor of paying his Rs25 yearly charge at Bank B. However, it isn’t substantial enough to warrant Bank-A’s Rs80 yearly charge. Someone with a “big” amount, on the other hand, would be motivated to select Bank A. So, what does it mean to be “large”? So, how big would his balance have to be to justify paying the yearly fee at Bank A in order to benefit from the lower interest rate?

**First, let’s compare Bank A to Bank B**

The difference between the two annual fees is Rs80 – Rs25 = Rs55.

The difference between the interest rates is 15% – 9% = 6%.

So, the balance would have to be large enough that a 6% rate applied to it for a year would be at least equal to Rs55. Solving, we get I = PRT; Rs55 = P (0.06) (1); P = Rs916.67

So, we can conclude that the cutoff for choosing Bank A over Bank B is Rs916.67, as at this balance annual charges of A & B will be the same and lesser than C.

Bank-A = (916.67 x .09) + 80 = Rs162.5

Bank-B = (916.67 x .15) + 25 = Rs162.5

Bank-C = (916.67 x .2399) + 0 = Rs219.91

**Credit card Balance Transfer Facility (BTF)**

If you owe money on your credit card and want to pay it off in installments, but your bank charges an exorbitant markup? Or do you want to simply transfer your debts from one credit card to another and pay with the bill from the new card? To achieve these goals, you can use a credit card’s Balance Transfer Facility (BTF).

You can transfer your outstanding amount from one credit card(s) to another using the BTF function. You have the option of paying in whole or in equal monthly payments. In this section, we will explain what the fees are for utilizing BTF and how you may calculate them before using the service.

When you move your dues from one card to another, the bank charges you a BTF processing fee and a markup until the dues are paid in full. The BTF processing cost is set, whereas the bank adds daily service fees and annual service fees on the total amount until you complete the final payment.

Assume you owe Rs10,000 on your Bank-A credit card and want to transfer the balance to your Bank-B credit card. For Bank-B Cards, the BTF processing fee is now Rs600/- or 2.5 percent of the transaction value, whichever is higher. In this case, it will be Rs600 because 2.5 percent of the amount you’re sending (Rs10,000) is Rs250, which is less than Rs600.

Second, Bank-B Annual Service Charges for BFT are 24 percent, thus multiply 24 percent by Rs. 10,000 and divide by 365 days to get the daily markup. This is performed in the following manner:

One-day service charges: (24 % / 365) x 10,000 = Rs. 6.58

Service costs for ten days are as follows: (24% /365) x 10,000 x 10 = Rs. 65.8

As a result, the costs would be Rs. 600 and Rs. 6.58 each day until full payment is made.

Every bank has its own BTF processing price and Annual Service Fee, while others provide simple monthly payments of 3, 6, 9, or 12 months with no markup and a processing fee depending on the plan and balance amount. You can still convert your transferred amount if the bank does not offer convenient monthly payments on the Balance Transfer Facility, but you will be charged a markup based on the bank’s fee schedule.