It’s no secret that credit cards can be useful to both businesses and individual consumers. It’s also no secret that letting things get out of control with credit cards can be disastrous to your financial well-being. Given these facts, it is worthwhile and important to have a solid understanding of the mathematics involved in their use.

**A Credit Card Explained: What
Is It Really?**

Credit cards are a handy and
flexible way to pay for items using the bank's credit facility (borrowed
money). Swiping your credit card through the payment machine at the gas/petrol
pump may not seem like you're taking out a loan, but in fact, you are borrowing
each time for every transaction. The bank (or any other financial institution)
that issued your card makes the payment to the gas station on your behalf, and
you repay them later to the bank. You are the borrower, and the financial
institution is the lender. People do use credit cards to purchase items that
they do not have the cash to pay for in full. However, there are several
additional reasons to use a credit card to pay for anything other than the
requirement to borrow the money to pay. You may be able to pay with cash at the
gas station or shopping mall, but you prefer to use a credit card since it is easier
to pay at the pump. Using a credit card to pay for Internet transactions is
typically far more convenient than other methods. In addition, for some
expenditures (such as hotel rooms and vehicle rentals), using a credit card may
eliminate the need to leave a hefty deposit. Other motivations to use a credit
card include “cash back” or frequent flyer mile incentives provided by some
card issuers. Regardless of your motivations, using a credit card involves borrowing
money, whether you intend to do so or not.

Because using a credit card
entails borrowing money, it also involves paying interest. One typical
criticism about credit cards is that their interest rates are sometimes quite
expensive when compared to other loans, such as the automobile or home loans. However,
car loans or house loans are collateralized loans. This implies that if you do
not return the loan on time, the lender has the authority/right to repossess
the property for which you borrowed the funds. The collateral for a vehicle
loan is the automobile; the collateral for a mortgage or home equity loan is
the house. 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 due to it, 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.

**1.
****Interest
Calculation and Average Daily Balance**

The computation of credit card
interest might be difficult. On the one hand, since statements are generated
and payments are due on a monthly basis, it makes it reasonable to compute and
charge interest to the account on a monthly basis. However, because the balance
varies from day to day, it appears that interest should be computed 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.

What should we use as the
principal if we're going to compute my interest monthly? The amount at the end
of the month was Rs2,200 (500+300-200+1,600). But it doesn't seem fair to
charge a whole month's interest on Rs2,200, especially because my balance was
considerably lower until one day at the end of the month. The amount at the
beginning of the month was Rs500 but retaining it as the principle would ignore
the larger balances that accumulated over the month.

There are several methods for calculating interest on a credit card, but the most popular is the average daily balance (ADB) approach. Interest is calculated and applied to the account monthly using the ADB technique, and the question of principal is answered by charging interest on the average of the daily amounts during the month. This appears to be a reasonable approach to the problem of changing balances.

**Average Daily Balances
Calculation of Credit Cards**

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

*ADB = Rs21,000/30 = Rs700*

**Calculating Credit Card
Interest**

Once we have calculated the
ADB, calculating the credit card interest is simple. Because there is no
compounding during the billing month, we may apply the basic interest formula
with the ADB as the principal. One possible stumbling block is the passage of
time. T can be conceived of as a month (therefore T = 1/12) or as the number of
days in the billing period, in which case 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
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.

**2.
****Interest
on Credit Cards—The Grace Period**

A grace period is a feature
that most credit cards offer, and it adds a unique element to the interest
issue. The grace period is a period of time that usually lasts 20 to 25 days
and *begins on the billing date of the card*. You pay no interest if you
pay the entire debt within the grace period and if you paid off your previous
month's balance in full (such that none of your balance is a carryover from the
previous month). This can save a lot of money for those who use their credit
card solely for convenience. Many people have credit cards that they use on a
daily basis but do not pay any interest on. Convenience users are the term used
in the business to describe such credit card customers. 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**

The due date for Nomi's credit
card is the 18th of every month, for example. His credit card has a 21.99
percent interest rate and a 20-day grace period. His account balance on October
18 was Rs935.14. On October 20, he charged Rs56.65; on October 29, he charged Rs309.25;
on November 9, he charged Rs81.17; and on November 17, he charged Rs101.42. On
November 3, he paid Rs935.14. How much interest would he owe if he settles the
debt on his November 18 statement in full before the grace period ends?

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. The answer
is: Rs0!

**3.
****Other
Fees and Expenses on Credit Cards**

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 maybe
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.

**4.
****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**

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

**5.
****Balance
Transfer Facility (BTF) on credit cards**

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.

For example, suppose you owe
Rs10,000 on your Bank-A credit card and wish to transfer it to your Bank-B
credit card. The BTF processing charge for Bank-B Cards is now Rs600/- or 2.5
percent of the transaction value, whichever is greater. It will be Rs600 in
this situation since 2.5 percent of your transferring amount (Rs10,000) is
Rs250, which is less than Rs600.

Second, Bank-B Annual Service
Charges for BFT are 24 percent, therefore you can compute the daily markup by
multiplying 24 percent by Rs. 10,000 and dividing by 365 days. This is
accomplished as follows:

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 a distinct BTF processing cost and Annual Service Fee for BTF, and some banks also provide simple monthly payments of 3, 6, 9, or 12 months with no markup and a processing fee based on the plan and balance amount. If the bank does not provide easy monthly payments on the Balance Transfer Facility, you can still convert your transferred amount, but you will be charged a markup based on the bank's fee schedule.

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For credit card users.