APR ↔ APY (Effective Rate) Converter

About the APR ↔ APY (Effective Rate) Converter

A rate of 6% a year paid as 0.5% every month grows money by more than 6% in a year, because each month’s interest earns interest too. The 6% is the nominal rate, or APR; the 6.1678% a year it really adds up to is the effective rate, called the APY (annual percentage yield) on savings and the effective annual rate (EAR) on loans.

This converter turns one into the other for daily, weekly, every-two-weeks, monthly, quarterly, half-yearly, yearly or continuous compounding, and shows the same rate at every other frequency, so a deposit compounded quarterly can be compared with one compounded monthly. It also turns a rate per period, such as a credit card’s 3.75% a month, into yearly rates, and works out a deposit’s APY from the interest it actually earned, with the formula of the US Truth in Savings rules. Every step is shown, and nothing leaves your browser.

Common uses

• Compare a savings account compounded monthly with a deposit compounded quarterly.
• See what a loan’s nominal rate, or a card’s monthly rate, costs in a year.
• Check the APY a bank shows against the interest it actually paid.
• Convert a quarterly rate into an equivalent monthly rate for a spreadsheet or another calculator.

The formulas

With the nominal rate as a decimal (6% = 0.06) and m compounding periods a year:

• APY = (1 + APR ÷ m)^m − 1
• APR = m × ((1 + APY)^(1/m) − 1)
• Rate per period = APR ÷ m, so 6% compounded monthly is 0.5% a month
• Continuous compounding: APY = e^APR − 1, and APR = ln(1 + APY)

Daily compounding uses 365 periods, weekly 52 and every two weeks 26. The more often a positive rate is compounded, the higher its APY, but the gain shrinks fast: 6% gives 6.1678% monthly, 6.1831% daily and 6.1837% continuously.

APR, APY and the effective annual rate

• APR is the nominal yearly rate. For US loans, Regulation Z makes the APR “the unit-period rate × the number of unit-periods in a year” — the monthly rate × 12 for monthly payments (appendix J). Fees are part of that APR; use the APR calculator for a loan with fees.
• APY is the effective yearly rate of a deposit: what it really earns in a year. US banks state it for deposit accounts under Regulation DD (Truth in Savings), which gives the formula in its appendix A.
• Effective annual rate (EAR) is the same idea for any rate. In the UK and the EU the APR of a credit agreement is itself an effective rate: it equates the present values of the money lent and the repayments “on an annual basis”, with a year of 12 equal months (FCA CONC App 1.2.6R). A UK APR is therefore compared with the APY here, not with the APR.

APY from the interest a bank paid

Regulation DD works the APY out from the interest a deposit earns: APY = 100 × [(1 + Interest ÷ Principal)^(365 ÷ Days in term) − 1], where Principal is the amount deposited at the start, Interest the total interest earned on it over the term, and Days in term the actual number of days (appendix A, part I). An account without a fixed term is treated as a 365-day term, so its APY is simply Interest ÷ Principal. The regulation’s examples: 61.68 earned on 1,000 in a year is 6.17%; 30.37 earned on 1,000 in a 182-day term is 6.18%.

Limitations

• Fees, taxes and penalties are not included: the APY here is what the interest rate alone gives.
• The rate is assumed to stay the same for the whole year; a variable rate gives a different result.
• Daily compounding uses 365 days a year. A bank that counts days differently gets a slightly different APY; enter its rate per period and periods with Rate per period if you know them.

Privacy

Everything is calculated in your browser. The rates and amounts you enter are never uploaded or stored.