Annual percentage yield is the rate U.S. banks and credit unions must quote for savings accounts, money market accounts and certificates of deposit under the Truth in Savings Act (Regulation DD). Regulation DD defines APY as a percentage rate reflecting the total amount of interest paid on an account, based on the interest rate and the frequency of compounding for a 365-day period. The plain interest rate, by contrast, is the annual rate that does not reflect compounding. Because APY folds compounding in, it puts accounts that compound daily, monthly or quarterly on the same footing, which makes it the number to use when comparing deposit accounts.
Formula
Regulation DD, Appendix A, gives the general formula:
APY = 100 × [(1 + Interest / Principal)^(365 / Days in term) − 1]
- Principal: the amount assumed to be deposited at the start of the term.
- Interest: the total dollar interest earned on that principal for the term.
- Days in term: the actual number of days in the term.
For a nominal rate r compounded n times a year, the same idea reduces to APY = (1 + r/n)^n − 1.
Example
A $10,000 deposit at a 4.00% interest rate compounded daily earns about $408.08 in 365 days:
- APY = 100 × [(1 + 408.08 / 10,000)^(365/365) − 1] ≈ 4.08%
The same 4.00% rate compounded monthly gives an APY of about 4.07%. A 182-day CD that pays $200 on $10,000 has an APY of 100 × [(1.02)^(365/182) − 1] ≈ 4.05%.
The CD calculator and compound interest calculator show how APY turns into dollars over a full term.
APY vs APR
APY is a savings term; APR is a borrowing term that measures the cost of credit. A higher APY is better for a saver, while a lower APR is better for a borrower. The CD vs high-yield savings guide compares accounts using APY. The mechanism behind the gap between rate and APY is compound interest.