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 actually borrowing each time you

make a transaction. The bank (or other financial organisation) 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. Credit cards are

used by people 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

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

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

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 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

total principal amount i.e., ADB

**R **is

rate in annual interest percent

**T** is

time period 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 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 onto 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

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 required to pay on or before

November 6). Whereas, if he pays the November balance in full on or before due

date plus the applicable grace period, he will owe no interest.

**Other Credit Card Fees and**

Expenses

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 possibilities to spend substantially

less for 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

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)

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.