Is the APY always greater than or equal to APR?
The Correct Answer and Explanation is:
Yes, the APY (Annual Percentage Yield) is always greater than or equal to the APR (Annual Percentage Rate), assuming that the interest is compounded.
Here’s why:
APR represents the interest rate without taking into account the effects of compounding. It is the simple interest rate applied over a year. For example, if you borrow $100 at an APR of 10%, you’ll owe $110 at the end of the year. This rate does not consider how frequently interest is added to the principal throughout the year.
APY, on the other hand, takes into account the interest earned on the initial principal as well as the interest that has already been added (compounding). The more frequently interest is compounded (e.g., daily, monthly, quarterly), the higher the APY will be, since the interest earned gets reinvested and itself earns additional interest.
If interest is compounded at least once during the year, APY will always be greater than APR. This is because the interest earned on the initial amount is added to the principal, and then this new total becomes the basis for the next calculation of interest.
The relationship can be mathematically described as:APY=(1+APRn)n−1APY = \left(1 + \frac{APR}{n}\right)^n – 1APY=(1+nAPR)n−1
Where n is the number of compounding periods per year. If n > 1, the APY will be greater than the APR. For instance, if the APR is 10%, and interest is compounded monthly (12 times a year), the APY will be about 10.47%.
So, if you only have simple interest (no compounding), then APR and APY will be the same. But when compounding occurs, APY will always exceed APR.
