To understand how to calculate APR, one must know the difference between APR and interest rate. APR is short for annual percentage rate, which is the actual amount of interest charged annually after compounding and expressed as a percentage, while interest rate is the stated, or quoted, rate assuming no interest compounding during the year. Thus, APR sometimes is called the compounded interest rate, and the interest rate as stated often is referred to as the simple interest rate. Therefore, how to calculate APR is based on both the chosen compounding method and the given simple interest rate.
Interest may be compounded yearly, semiannually, quarterly, monthly, daily, or at any other time frequency. Such time intervals are the so-called compounding periods, a basic element in interest compounding. How to calculate APR directly relates to interest compounding, which means calculating interest once every compounding period by multiplying the given simple interest rate to the principal amount, and then including the calculated interest charge into the current outstanding balance to arrive at the principal balance for the next compounding period.
For any stated, or given, interest rate, the more frequent interest is compounded during a year, the higher the total interest charge will be at the end of a year and thus, the higher the APR becomes. In most cases, the actual APR will be higher than the quoted interest rate. However, APR will equal interest rate as quoted if interest is compounded only once a year.
Periodic Interest Rate
Having decided on the interest compounding period, how to calculate APR becomes a matter of applying the given interest rate to the outstanding principal balance. However, the interest rate as quoted cannot be directly used in the calculation because it is expressed as an annual percentage while the interest compounding period is likely not on an annual basis. Therefore, the quoted interest rate must be first converted to the so-called periodic interest rate with the same time horizon as the interest compounding period. For example, how to calculate APR semiannually for the quoted interest rate of 10 percent requires the conversion of the annual rate to a periodic semiannual interest rate of five percent.
How to Calculate APR
Assuming the principal amount is $100 at the beginning of a period, the quoted interest rate is 10 percent, and that interest is compounded semiannually, or twice a year. How to calculate APR thus involves the following computations. Covert the annual interest rate of 10 percent to a semiannual rate of five percent (10 percent/2 = 5 percent). Multiply the $100 principal by the periodic semiannual rate of 5%, and get $5 in interest. Add the $5 interest to the $100 principal and get $105 in outstanding balance. Multiply the $105 again by 5%, and the compounding interest is $5.25. As a result, the annual total interest charge is $10.25 ($5 + $5.25) on a $100 starting principal, which equals an annual percentage rate, or APR, of 10.25 percent ($10.25/$100), higher than the quoted interest rate of 10 percent.
The calculations will be much more complicated if interest compounds on a more frequent basis, say, daily, and a financial calculator may be needed.