How to Calculate Credit Card Payments

Credit cards are one alternative when making purchases to buy things without needing cash. However, like any debt, credit card debt is a promise to pay more than what was borrowed in exchange for this convenience. Credit card companies fix interest rates to not only earn a return on their investment, but to also compensate themselves for the risk that the money will not be repaid. This is why credit card holders with low credit ratings must pay higher interest rates; they are a higher risk for the credit card company.

With credit card debt on the rise, credit card holders may wish to reduce or eliminate their credit card debt. Credit card debt can adversely affect a credit rating because the more debt a person holds, the higher a risk they are for other lenders. Reducing credit card debt not only puts credit card holders in a better financial position, it also makes them a better credit risk to lenders. This can be important when credit card holders are considering a major purchase such as a house or a car. Interest over long periods of time has a huge impact on the value of debt to both the borrower and lender. For long-term borrowing such as a car loan or a mortgage, lower interest rates can reduce payments by thousands if not tens of thousands over the life of the loan.

Suppose that a credit card holder has $5,000 in credit card debt on a card that carries a 12% APR interest rate. The cardholder wants to know what monthly payments are needed to pay the debt off in 3 years. The problem with this type of calculation derives from the compounding frequency of interest. Interest may accrue annually, semi-annually, quarterly, monthly, weekly, or even continuously. Typically, credit card interest is compounded monthly, so for our example here we will make this assumption.

Figuring the time to pay off debt is a matter of using time value of money formulae. In this case, the monthly payments will be paid regularly (each month) and will be the same amount for each payment. In finance, this type of payment is known as an annuity. An annuity is simply any payments which are equal and occur at regular intervals. Other types of annuities include disability insurance, structured settlements, and payments made from lottery winnings. To find out the payments needed to get out of interest-accruing debt, we use a two-step process.

The Future Value of an Annuity formula is often used in financial management to calculate the value of an asset at some time in the future. This formula answers the question: what is this investment (or debt) worth in the future? The future value formula is given as:

FV = PV * (1 + r)ⁿ

where FV is the future value, PV is the present value, r is the interest rate, and n is the number of periods. For our example above, the present value is the value of the debt today or $5,000.00; this is the amount we would have to pay today to get completely out of debt. The interest rate above is given as 12% APR. Since interest is compounded monthly, we need to find out the interest rate per pay period. In this case it is 1% (12% / 12 months per year = 1% per month). If the interest rate were given as an APY, an APR would need to be calculated first. Since interest is compounded monthly and payments are made monthly, the number of periods is equal to 36 (3 years * 12 months per year = 36 pay periods). Using the formula above we have:

FV = 5000 * (1 + .01)³⁶

FV = 5000 * 1.4308

FV = $7,153.84

In other words, if no payments were made, the value of the $5,000 debt would be $7153.84 in three years at 12% APR with monthly compounding.

Now that we know the value of the debt in three years, (the time we wish to have the debt paid off), we want to figure the monthly payments needed to bring the future value of the debt to zero. We now need to use the present value of an annuity formula to find the payments. The present value of an annuity formula is given as:

PV = CF * [(((1 + r)ⁿ) – 1) / r]

where PV is the present value, CF is the cash flow (or monthly payments), r is the interest rate per period, and n is the number of periods. For our example, we must now think of the future value figured above ($7153.84) as the present value of the debt because it is the amount we would have to pay in three years were we not to make any payments at all. Plugging our numbers into the present value of an annuity formula we have:

7153.84 = CF * [(((1 + .01)³⁶) – 1) / .01]

7153.84 = CF * 43.0769

CF = $166.07

So, at 12% APR over three years with monthly compounding of interest, a cardholder would need to pay $166.07 per month over three years to pay off the $5,000 debt. Notice that the total amount paid would be $5,978.57 ($166.07 * 36). This gives an effective interest rate of about 19.57% ((5978.57 – 5000 / 5000)) over the course of three years.

The two steps given above can be used to figure the payments for any number of periods and any interest rate. For example, suppose we wanted to know the payments necessary to bring the debt to zero over one, two, three, four, and five years at the 12% APR interest rate. Using the two-step process above, we can figure out these payments as:

1 year = $444.24

2 years = $235.37

3 years = $166.07 (our example above)

4 years = $131.67

5 years = $111.22

Notice that the amount needed to pay off the debt as the number of periods increases does not follow a linear pattern. This is because of the term structure of interest rates. Essentially, cash flows far out into the future do not contribute much to the present value of debt (or an investment). Using this information wisely, a debt holder can figure out the payments that match what he/she is capable of paying.

The two-step process given above can be used to figure monthly payments for credit card debt to get the debt down to zero in a specified amount of time. There is actually a formula that can do the same calculation in one step, but it is quite cumbersome. It is often referred to as the Basic Calculator Formula because it is the one most commonly used by financial calculators to make time value of money calculations.

Getting out from under credit card debt is a process of planning and consistency. Making consistent payments is the key to getting that debt down to zero. Making erratic payments makes it difficult to calculate the time required to eliminate the debt, and it plays havoc with the interest paid on a monthly basis. Using the two-step process above, credit card holders can better plan for a reduction and eventual elimination of credit card debt by making regular and planned monthly payments.