Credit Cards - Example

Enter the client's credit card balance and hit the calculate button.  The chart shows the actual amount of interest in line one, what they could have earned in their other investments had they not given the interest away, and what the bank is earning.  

Using credit cards and not paying them off each month (before interest is charged) is a serious wealth transfer.  Often times, card companies do not charge an interest charge if the balance is paid in full each month.  They would not be in business if everyone did just that.  The reality of the situation is that the card companies are counting on a vast majority of users to carry a balance and/or make late payments.

If you carry a balance of $5,000 at 18% over 40 years you would have only given away $39,433 in lost interest.  Had you paid cash and invested the interest at 8% over a 40-year period you would have $255,383.  

Let’s change the example slightly.  If interest of 8% were changed to 18%, the card company would gain:

$6,680,280!

This is an obvious problem and one that must be avoided if one is going to accumulate any wealth.

The following example inputs are used in this help topic:

•Credit Card Balance               $5.000

•Credit Card Interest Rate        18% (compounded daily)

•Investment Return Rate          8%

Assumptions & Clarifications:

•We are dealing ONLY WITH THE INTEREST on credit card debt.

•We assume the credit card debt is held constant ($5,000 per year).

•The calculations of future value or opportunity cost is at end of period.

At first glance, the interest calculation on this screen may appear too high.  For example, the interest on a balance of $5,000 at 18% per year for five years is $1,971.61 as opposed to $1800. A quick, but wrong, calculation of the interest would be:

18% of $5,000 is $900 and

$900 x 5 years = $4,500.

We will show below that the correct answer is $4.929.10.

CALCULATION OF FIRST ROW

A correct calculation, or at least a calculation similar to that used by the credit card companies, uses the annual effective rate of interest. The annual effective interest rate takes into account the number of compounding periods in the year.  In the case of credit cards, compounding is usually done daily, so there are 365 compounding periods.

If we assume:

•365 days per year  (360 days is sometimes used)

•Daily compounding

Then the effective annual interest rate for some typical credit card nominal rates are:

Nominal        Effective Annual Rate

14%                15.0243%

16%                17.3470%

18%                19.7164%

20%                22.1336%

For 18 %, the Effective Annual Interest is equal to

((1+.18/365)^365) -1  = .197164  =  19.7164%

where the ^ means raise to a power or exponentiation.

Many financial calculators will convert a nominal rate of interest to an annual effective rate of interest.

For the example inputs:

The interest on the first year is $5,000 X 19.7164% = $5,000 X .197164 = $985.82.

For five years, the total interest will be 5 X $985.82 = $4.929.10.

Notice we are not compounding the interest, but just multiplying the interest per year times 5 years.

The interest is NOT compounded (annually) over the five-year period, since we assume the credit card debt is held constant.

CALCULATION OF SECOND ROW

The second row is calculated using the future value function with these inputs:

•annual compounding

•nominal interest rate (not effective).  

•payment per year is annual interest from the first row  

•end of period payments

For the example inputs:

Set begin/end to end

Set 5 periods (years)

Set an interest rate of 8%

Set a present value of $0

Set payments of -$985.82 (The minus sign just means cash outflow)

Calculate future value of $5,781.66.

CALCULATION OF THIRD ROW

The third row is calculated like the second row except the effective rate of interest is used.  The bank is making the effective rate from credit card loans.

For the example inputs:

Set begin/end to end

Set 5 periods (years)

Set the effective interest rate of 19.7164%

Set a present value of $0

Set payments of -$985.82 (The minus sign just means cash outflow)

Calculate future value of $7,295.27.