APR vs. APY: The Hidden Math in Bank Advertising
Calculate the true annual yield of any investment instantly using our APY Calculator, or read on to understand how banks use math to manipulate their marketing.
When you apply for a credit card, the bank advertises a 24% APR. When you open a high-yield savings account, the bank advertises a 5% APY.
Why do banks use two different acronyms that sound exactly the same? The answer lies in the mathematical power of compound interest. Banks use APR when they are charging you money, and APY when they are paying you money, to make their numbers look as attractive as possible.
What is APR (Annual Percentage Rate)?
APR is the simple interest rate over a one-year period. It completely ignores the effect of compounding within that year.
If a credit card has a 24% APR, the bank divides that by 12 months to get a 2% monthly interest rate.
However, credit cards compound interest daily. Because you are paying interest on top of previous interest every single day, the actual amount of interest you pay over the course of a year is mathematically higher than 24%. But the bank is legally allowed to advertise the lower, simpler number (24% APR) because it looks less scary to the consumer.
What is APY (Annual Percentage Yield)?
APY is the effective interest rate. It accounts for exactly how much money you will earn over a year after all the compounding has taken place.
If a savings account pays 4.9% simple interest, but it compounds daily, the APY will be roughly 5.02%.
Banks advertise the APY on savings accounts because factoring in the compound interest makes the number higher, which attracts more customers.
The Core Difference
- APR: Ignores compounding. It is the "stated" rate. (Makes high rates look smaller).
- APY: Includes compounding. It is the "true" rate. (Makes low rates look bigger).
The APY will always be mathematically higher than the APR as long as the compounding frequency is more than once a year.
How to Calculate APY from APR
If a bank offers you a loan and only tells you the APR, you should calculate the APY to find out the true cost of the debt.
The Formula:
APY = (1 + (APR / n))^n - 1
Where:
- APR is the stated rate (as a decimal)
- n is the number of compounding periods in a year (e.g., 12 for monthly, 365 for daily).
Example Calculation
A credit card advertises a 24% APR (0.24) that compounds daily (365). What is the true cost of the debt (APY)?
APY = (1 + (0.24 / 365))^365 - 1
APY = (1 + 0.0006575)^365 - 1
APY = (1.0006575)^365 - 1
APY = 1.2711 - 1
APY = 0.2711
The true cost of the credit card debt is 27.11% APY. By advertising the APR instead of the APY, the bank legally hid over 3% of annual interest from their marketing materials!
FAQ
Do mortgages use APY? No. By law in the United States, mortgages must be advertised using APR. However, mortgage APR is unique because it is required to include not just the interest rate, but also the broker fees, closing costs, and discount points, expressing the entire cost of the loan as a single yearly percentage.
Never accept a loan without knowing the true cost. Convert APR to APY instantly using the CalcUnit APY Calculator.