APR to APY conversion tables and rate references
Two numbers describe one interest rate, and which one you get handed depends on whether you are borrowing or saving. The tables below cover the conversion both ways: the period counts that feed the formula, the converted figure at the rates people actually quote, and the regulatory conventions that decide which figure a product is allowed to advertise.
Compounding frequency and the period count
The single input that changes a conversion result, aside from the rate, is n: how many times a year interest is calculated and credited. Parify exposes eight values. Higher n widens the gap between APR and APY.
At n of 1 the conversion is a no-op: annual compounding leaves APR and APY identical. Daily compounding using 365 ignores leap years; some agreements use a 360-day or actual-day basis, which shifts the result in the third decimal.
When a quote does not state its compounding period, these defaults match how each product usually behaves.
For a US deposit account, daily compounding credited monthly is the safe assumption. For installment loans, monthly matches the payment cycle and the way the lender accrues interest between statements.
APR to APY at common rates
Effective yield for a nominal APR, by frequency, using APY = (1 + APR/n)^n − 1. Read down your rate, across to your compounding period. Figures rounded to three decimals, the same precision Parify displays.
The spread you see in the right four columns is what Reg Z's nominal convention leaves off the headline rate. It barely registers at 2% and runs past three full points by the time you reach a revolving credit-card APR.
APY to APR at common rates
The reverse direction, APR = n × ((1 + APY)^(1/n) − 1). A single APY maps to a different APR at every frequency, so the period count is required, not optional. Use this when a quote arrives as an effective yield and you need the underlying nominal rate.
A 5.00% APY at daily compounding traces back to a 4.879% APR. The lower the n, the closer the nominal rate sits to the yield it produces.
How regulation decides which number gets quoted
Two federal statutes mandate opposite conventions for the same arithmetic. A loan must advertise the nominal figure; a deposit must advertise the effective one.
Because compounding only adds to an effective return, the lending convention always shows the smaller number and the savings convention the larger. A mortgage APR carries an extra wrinkle: under Reg Z it folds points and certain fees into the figure, so it sits above the note rate for reasons a pure compounding conversion does not capture.
Related concepts
- Nominal vs effective rate. The general-math names for what Reg Z and Reg DD call APR and APY: the stated per-period rate scaled up versus the rate after compounding is folded in.
- Day-count convention. Whether a year is treated as 365, 360, or actual days; it moves a "daily" result in the third decimal and varies by agreement.
- Continuous compounding. The limit as
ngrows without bound,APY = e^APR − 1. Daily compounding already lands within a rounding hair of it at ordinary rates. - Mortgage APR. A Reg Z figure that bundles points and fees, distinct from the compounding-only conversion here and usually higher than the note rate.
- Basis point. One hundredth of a percentage point; the unit the APR-to-APY spread is most naturally measured in.