Annual Percentage Rate (APR)
APR is the annual rate a consumer pays on a loan. APR has two defining characteristics:
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APR includes fees and other loan related costs in addition to the interest charged on the loan. This is important because it helps consumers get a more complete picture of the total cost of a loan.
- APR uses simple interest, not compound interest, in its calculation. Compound interest is interest earned on one’s interest. Because some loans compound their interest due, a consumer’s actual rate on their loan may be higher than the stated APR for the loan.
Where APR is Used
APR is most likely to be quoted when a consumer is looking for and evaluating different types of consumer loans such as a car loan, a mortgage loan or a loan on larger household purchases such as appliances. Consumers can compare APRs for similar types of loans. One could use APR to compare two different car loans to evaluate which of the loans would result in a lower total cost.
It’s important to recognize that APR is different and typically higher than the simple interest rate that may be quoted for a loan.
How an Annual Percentage Rate Works
APR has two key inputs:
- The fees and costs associated with the loan
- The interest costs of the loan
Once these two variables are known, the APR can be calculated.
APR Formula & Calculation
APR = [(((Loan Fees + Loan Interest) / P) / N) * 365] * 100
- Loan Fees = The total amount of all loan fees
- Loan Interest = The total interest owed over the life of the loan
- P = The Loan Principal, i.e. the amount of the loan
- N = the total number of days in the term of the loan
Let’s say that a consumer takes out a $1,000 loan to purchase a new refrigerator. The loan has the following characteristics:
- The loan principal is $1,000
- The interest rate of the loan is 7%
- The loan interest is $70 ($1,000 x 7%)
- There are $20 in total fees associated with the loan
- The loan has a term of 1 year
The consumer’s APR is calculated as follows:
APR = [(((20 + 70) / 1000) / 365) * 365] * 100 = 9%
So while the loan had an interest rate of 7%, the consumer will actually pay 9% due to the additional fees associated with the loan.
Key Takeaway: APR is a more accurate measure of a consumer’s loan cost.
Annual Percentage Yield (APY)
APY is the annualized investment return of an investment product and is typically used for savings accounts, money market accounts, and Certificates of Deposit (CDs). Note that unlike APR, APY does take into account compound interest.
Where is APY Used
Investors will most likely come across APY when they are reviewing and evaluating the rates of return of different types of bank accounts and CDs.
How an Annual Percentage Yield Works
The two inputs to APY are:
- The interest rate of the investment
- The frequency of compounding
The greater the frequency of compounding, the greater the APY.
APY Formula and Calculation
APY = [(1 + (i/N)) ^ N] – 1
- i = the stated annual interest rate of the investment product
- N = the number of compounding periods per year
Let’s say that an investor will purchase a $1,000 CD. The CD has an annual interest rate of 5% with daily compounding, so there are 365 compounding periods per year.
The investor’s APY is calculated as follows:
APY = [(1 + (0.05/365)) ^ 365] – 1 = 0.05127 or 5.127%
So while the CD had an interest rate of 5%, the investor will actually receive 5.127% due to compound interest.
APR vs. APY for Interest Rate
When evaluating loans, consumers will generally favor loans with lower APRs since they will pay total lower fees and interest on their loan. In contrast, when looking for savings and investment products, investors will generally favor investments with higher APYs since they will realize a higher return on their investment.
APY vs. APR vs. EAR
Effective Annual Rate (EAR) is another way to measure the cost of a loan or the return of an investment product. EAR accounts for compound interest thus making it potentially more accurate than APR if interest owed compounds on a more frequent basis than annually. EAR is thus more reflective of the “all-in” loan costs for a borrower.
In terms of investments, EAR is synonymous with APY since they both take into account compound interest.
Converting APR to APY
It is possible to convert APR to APY. If one was provided an APR and the compounding frequency of the interest, an APR could be converted to an APY to obtain a better estimate of the total cost of a loan.
APR and APY are related by the following formula:
APY = [(1 + (APR/N)) ^ N] – 1
- N = the number of compounding periods in a year
Let’s say that a consumer has a car loan with an APR of 4% and the loan’s interest compounds daily (365 compounding periods in a year).
The consumer’s car loan APY would be:
APY = [(1 + (.04/365)) ^ 365] – 1 = 0.0408 or 4.08%
Key Takeaway: Converting the consumer’s APR to an APY provides a more accurate cost of the loan since APY takes into account the compounding of the loan’s interest.
Bottom Line
Consumers can use APR to compare similar loan options and investors can use APY to compare the returns on similar investments. All other things being equal, consumers will generally favor lower APR loans and investors will generally favor higher APY investments.
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