Whether you're taking out a loan to purchase a new car or using a credit card to make purchases, lenders generally advise you of the nominal, or stated, interest rate you'll pay on balances. However, when repaying a loan you'll usually end up paying a higher percentage of interest than the nominal rate you're quoted -- known as the effective rate. The difference between the two is the result of the compounding periods that the effective interest rate takes into account.
Compounding Is the Main Difference Between Rates
Compounding periods refer to the number of times per year interest charges are calculated and added your outstanding balance. Most credit card companies, for example, compound interest on a monthly basis -- meaning they increase your outstanding balance by one-twelfth of the annual interest rate each month. In other words, if your credit card offers a 12-percent interest rate but it compounds monthly, your balance will increase by one percent each month. The 12-percent rate is the nominal rate, which gives you a monthly nominal rate of one percent.
Effective Interest Rates & Capitalization
When a loan balance is compounded monthly, you're actually paying more than 12 percent each year -- the precise amount being the effective interest rate. Effective interest rates take into account the number of compounding periods and the fact that interest is capitalized after each period.
Capitalization means that the interest charges applied after each period increase the debt balance subject to interest during the next compounding interval. Put simply, interest is charged on prior interest charges if not paid off by the next compounding interval. For example, if your balance at the end of the first month is $1,000 and you're charged one percent interest, or $10, the balance used to calculate interest at the end of the second month is $1,010. In this example, the lender is charging interest on interest -- and effective interest rates reflect the true rate of interest you're paying at the end of the year because of this.
Calculating Effective Interest Rates
If you know what the nominal, or stated, rate of interest is, you can figure out what your effective rate is with the following formula:
Effective Interest Rate (EIR) = (1 + a / b)b – 1
a = nominal rate of interest expressed as a decimal (i.e. enter .10 for 10%)
b = number of compounding periods in one year
Credit Card Example
To illustrate how this works, suppose you transfer a $10,000 balance to a new credit card that offers an introductory interest rate of 9 percent for the first year, compounded on a monthly basis. Your effective interest rate is calculated as:
EIR = (1 + .09/12)12 – 1
= (1.0075)12 – 1
= 1.0938 – 1
= .0938 or 9.38%
The effective interest rate is 0.38 percent higher than the advertised nominal rate. If you maintain the $10,000 balance throughout the year, you'll actually pay $938 in interest -- not the $900 you'd arrive at when using just the nominal rate.