What is APR and APY, and What's the Difference?

What is APR and APY, and What's the Difference?

The annualized percentage yield (APY) of a loan takes into account the effect of compounding interest during the loan period, meaning that it reflects the interest earned by previously accumulated interest. Annualized percentage return (APR) is a simpler figure that does not include compound interest. Due to this discrepancy, banks and credit unions use APR and APY for different purposes in their marketing.

APR: Annualized Percentage Rate

The APR of a loan is equal to the periodic rate multiplied by the number of periods in each year:

APR = periodic interest rate x total number of periods

This simple calculation gives an approximation of the rate of interest accumulated over one year, but it does not account for the additional sums earned by previous interest payments, a mechanism called compounding.

Take the example of a loan that costs the borrower 1.00% in interest each month. The APR of the loan would come out to 12.00% —but so would the APR of a different loan earning 12.00% once every 12 months. Although the loan compounded monthly will accrue more interest than the loan compounded annually, the two have the same APR because compound interest is not included in this figure.

In most cases, you can expect to pay an actual rate slightly above the APR that is advertised for a loan or credit account. The more often a loan's interest is compounded each year, the more APR will fall short of the actual interest rate of the loan.

APY: Annualized Percentage Yield

In contrast to APR, the APY of a loan includes the amount earned from compounding. Mathematically:

APY = (1 + periodic interest rate)^(total number of periods) - 1

For a theoretical loan that earns 1% interest monthly, the APY equals 12.68%, a slightly higher figure than its APR of 12.00%. Once again, the difference here is explained by the fact that APY calculates not only the interest rate earned by the initial amount of the loan (principal) but also the interest earned by previously accumulated interest.

In effect, the earnings from one month are added to the principal and go on to earn even more interest in the next month. Therefore, APY, which measures this effect, represents the cost of borrowing more accurately than APR does.

How Banks Use APR and APY

When you browse through the different accounts, loans and credit cards offered by a bank or credit union, you will find that APR is used to describe loans, credit cards and other products which involve the customer as a borrower, while APY is commonly attached to those in which the customer is earning interest as a lender.

For example, a customer's possible earnings from savings accounts and CDs will always be described in terms of APY, since customers are seeking to earn the highest rate possible on their own money.

On the other hand, APR is always lower than the actual rate of paid interest, so banks often use it to market products in which customers are looking for the lowest interest rates. These include credit card agreements, mortgages and personal loans.

The Truth in Lending Act of 1968 sets the standards on how lenders like banks and credit unions are allowed to market their products. The law seeks to protect consumers by enabling an "apples-to-apples" comparison for all similar products available in the market, as well as to prevent the deceptive or overly complicated presentation of interest rates. For instance, we used APY as a common measure to help determine the best savings accounts available to consumers.

Calculating the Difference Between APR and APY

The difference between the APR of a loan and its APY grows larger the more often the interest gets compounded. Consider the effect of compounding on the APY of a loan with an advertised APR of 10.00%:

Yearly (1)10.00%10.00%
Semi-Annually (2)10.00%10.25%
Quarterly (4)10.00%10.38%
Monthly (12)10.00%10.47%

While even an extra 0.47% per year may seem small on its own, certain loans, like home mortgages, can involve hundreds of thousands of dollars accruing interest over several decades. Both the amount and duration of a loan can magnify the effect of compound interest into a force with significant bearing on your financial plans.

Accounting for Inflation: the Real Interest Rate

While compound interest adds to the cost of a loan, the constant effect of inflation works in the opposite direction. As currency loses value over time and more dollars are required to purchase the same goods and services, the money involved in a loan also loses value.

Calculating the effect of inflation on the interest rate of a loan results in a figure called the real interest rate, which is roughly equal to the difference between a loan's advertised interest rate, called the nominal rate, and the rate of inflation:

Real Interest Rate = Nominal Interest Rate - Inflation Rate

The nominal interest rate can be either APR or APY, although APY will result in a slightly more accurate calculation. If the annual inflation rate is 1%, then a 1-year loan which has an APY of 10% will earn a real interest rate of 9%. This signifies the fact that although the lender has profited from the interest on the loan, the actual purchasing power of that profit has decreased due to the inflation of the currency.

The real interest rate of a loan is always an estimate because it is impossible to know how the future rate of inflation will behave over the course of the loan. However, calculating the real interest rate is useful if you are a lender determining whether or not a certain investment is worth the time it will take to yield a return.