Annual Interest Rate Definition
The Annual percentage rate (APR) of a loan is the yearly interest rate expressed as a simple percentage. A bank or lender quotes the rate or APR. The annual percent rate does not incorporate the effects of compounding.
The federal Truth in Lending Act requires all consumer loan agreements to show the APR in large bold type. This is to make it easier for consumers to compare borrowing costs from different lenders. However, the annual percentage rate may not be the most accurate representation of the cost of the loan.
If interest on the loan compounds more than once per year, then the annual percent rate will be less than the actual interest rate on the loan, which is called the effective interest rate or the effective annual rate (EAR). In order to see the true cost of the loan, it is necessary to convert the annual percentage rate into the effective annual rate.
Annual Interest Rate Equation
If the lender offers a loan at 1% per month and it compounds monthly, then the annual percentage rate (APR) on that loan would be quoted as 12%. The annual percentage rate does not include the effects of compounding, so it is less than what the borrower would actually pay. Below is the annual interest equation for APR.
12% = 1% per month x 12 months
APR = Rate per period x Periods per year
Effective Annual Rate Formula
If the lender offers a loan at 1% per month, and the loan compounds monthly, the effective annual rate (EAR) on that loan would be 12.68%. The effective annual rate does include the effects of compounding, so it is higher than the APR. The EAR reflects what the borrower actually pays in interest on the loan. Below is the effective annual rate formula.
12.68% = (1 + 1%)12
EAR = ( 1 + (APR/N)N ) – 1
(Where N = the number of compounding periods per year.)
Convert APR to Monthly Interest
To convert annual rate to monthly rate, when using APR, simply divide the annual percent rate by 12.
Monthly Rate = APR / 12
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