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
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
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)
total principal amount i.e., ADB
rate in annual interest percent
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
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
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
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.
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
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.)
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 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
First, let’s compare Bank A to
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 =
Bank-B = (916.67 x .15) + 25 =
Bank-C = (916.67 x .2399) + 0=
Credit card Balance Transfer
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
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
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.