The formula
APY = (1 + nominal ÷ n)^n − 1
Where it comes from
The nominal rate ignores compounding: it is simply the periodic rate multiplied up. The effective rate folds the compounding back in, and it is the only figure that lets you compare two products honestly. Fees push it up further on borrowing.
How to work it out by hand
- Divide the nominal rate by the number of compounding periods
- Add 1 and raise to the power of that number of periods
- Subtract 1 and multiply by 100
- For a loan, spread any fees across the term and add them in
What is worth knowing
The gap grows with the rate and with the frequency, but it saturates quickly: 6% compounded monthly gives 6.17%, daily gives 6.18%, and continuously 6.18%. So a bank advertising daily compounding is offering you a rounding error over monthly. Fees are the part that actually moves the number, particularly on short loans, because an arrangement fee is spread over fewer periods. Terminology varies by market: the US uses APY for savings and APR for loans, where APR by law includes most fees; Europe uses TAE or AER for the same idea. Whatever it is called, compare like with like.