how the annual percentage rate apr works
an annual percentage rate is expressed as an interest rate it calculates what percentage of the principal you ll pay each year by taking things such as monthly payments and fees into account apr is also the annual rate of interest paid on investments without accounting for the compounding of interest within that year the truth in lending act tila of 1968 mandates that lenders disclose the apr they charge to borrowers 1 credit card companies are allowed to advertise interest rates on a monthly basis but they must clearly report the apr to customers before they sign an agreement 2credit card companies can increase your interest rate for new purchases but not existing balances if they provide you with 45 days notice first 3apr is calculated by multiplying the periodic interest rate by the number of periods in a year in which it was applied it does not indicate how many times the rate is actually applied to the balance apr fees interestprincipaln 365 100where interest total interest paid over life of the loanprincipal loan amountn number of days in loan term begin aligned text apr left left frac frac text fees text interest text principal n right times 365 right times 100 textbf where text interest text total interest paid over life of the loan text principal text loan amount n text number of days in loan term end aligned apr nprincipalfees interest 365 100where interest total interest paid over life of the loanprincipal loan amountn number of days in loan term types of aprscredit card aprs vary based on the type of charge the credit card issuer may charge one apr for purchases another for cash advances and yet another for balance transfers from another card issuers also charge high rate penalty aprs to customers for late payments or violating other terms of the cardholder agreement there s also the introductory apr a low or 0 rate with which many credit card companies try to entice new customers to sign up for a card bank loans generally come with either fixed or variable aprs a fixed apr loan has an interest rate that is guaranteed not to change during the life of the loan or credit facility a variable apr loan has an interest rate that may change at any time the apr borrowers are charged also depends on their credit the rates offered to those with excellent credit are significantly lower than those offered to those with bad credit apr does not take into account the compounding of interest within a specific year it is based only on simple interest apr vs annual percentage yield apy though an apr only accounts for simple interest the annual percentage yield apy takes compound interest into account as a result a loan s apy is higher than its apr the higher the interest rate and to a lesser extent the smaller the compounding periods the greater the difference between the apr and apy imagine that a loan s apr is 12 and the loan compounds once a month if an individual borrows 10 000 their interest for one month is 1 of the balance or 100 that effectively increases the balance to 10 100 the following month 1 interest is assessed on this amount and the interest payment is 101 slightly higher than it was the previous month if you carry that balance for the year your effective interest rate becomes 12 68 apy includes these small shifts in interest expenses due to compounding while apr does not here s another way to look at it say you compare an investment that pays 5 per year with one that pays 5 monthly for the first month the apy equals 5 the same as the apr but for the second the apy is 5 12 reflecting the monthly compounding given that an apr and a different apy can represent the same interest rate on a loan or financial product lenders often emphasize the more flattering number which is why the truth in savings act of 1991 mandated both apr and apy disclosure in ads contracts and agreements 4 a bank will advertise a savings account s apy in a large font and its corresponding apr in a smaller one given that the former features a superficially larger number the opposite happens when the bank acts as the lender and tries to convince its borrowers that it s charging a low rate a great resource for comparing both apr and apy rates on a mortgage is a mortgage calculator let s say that xyz corp offers a credit card that levies interest of 0 06273 daily multiply that by 365 and that s 22 9 per year which is the advertised apr now if you were to charge a different 1 000 item to your card every day and waited until the day after the due date when the issuer started levying interest to start making payments you d owe 1 000 6273 for each thing you bought to calculate the apy or effective annual interest rate the more typical term for credit cards add one that represents the principal and take that number to the power of the number of compounding periods in a year subtract one from the result to get the percentage apy 1 periodic rate n 1where n number of compounding periods per year begin aligned text apy 1 text periodic rate n 1 textbf where n text number of compounding periods per year end aligned apy 1 periodic rate n 1where n number of compounding periods per year in this case your apy or ear would be 25 7 1 0006273 365 1 257 begin aligned 1 0006273 365 1 257 end aligned 1 0006273 365 1 257 if you only carry a balance on your credit card for one month s period you will be charged the equivalent yearly rate of 22 9 however if you carry that balance for the year your effective interest rate becomes 25 7 as a result of compounding each day apr vs nominal interest rate vs daily periodic ratean apr tends to be higher than a loan s nominal interest rate that s because the nominal interest rate doesn t account for any other expense accrued by the borrower the nominal rate may be lower on your mortgage if you don t account for closing costs insurance and origination fees if you end up rolling these into your mortgage your mortgage balance increases as does your apr the daily periodic rate on the other hand is the interest charged on a loan s balance on a daily basis the apr divided by 365 lenders and credit card providers are allowed to represent apr on a monthly basis though as long as the full 12 month apr is listed somewhere before the agreement is signed disadvantages of annual percentage rate apr the apr isn t always an accurate reflection of the total cost of borrowing in fact it may understate the actual cost of a loan that s because the calculations assume long term repayment schedules the costs and fees are spread too thin with apr calculations for loans that are repaid faster or have shorter repayment periods for instance the average annual impact of mortgage closing costs is much smaller when those costs are assumed to have been spread over 30 years instead of seven to 10 years lenders have a fair amount of authority to determine how to calculate the apr including or excluding different fees and charges apr also runs into some trouble with adjustable rate mortgages arms estimates always assume a constant rate of interest and even though apr takes rate caps into consideration the final number is still based on fixed rates because the interest rate on an arm will change when the fixed rate period is over apr estimates can severely understate the actual borrowing costs if mortgage rates rise in the future mortgage aprs may or may not include other charges such as appraisals titles credit reports applications life insurance attorneys and notaries and document preparation there are other fees that are deliberately excluded including late fees and other one time fees all this may make it difficult to compare similar products because the fees included or excluded differ from institution to institution in order to accurately compare multiple offers a potential borrower must determine which of these fees are included and to be thorough calculate apr using the nominal interest rate and other cost information 