Why use this calculator
Two products quoting the same headline rate can pay or cost noticeably different amounts, and the reason is almost always compounding frequency. A savings account advertising 5 per cent paid monthly returns more over a year than one paying 5 per cent annually, because each month's interest starts earning immediately.
On the borrowing side the same effect works against you: a credit card quoting a nominal annual rate but applying a daily periodic rate costs more than the headline suggests. Regulators know this, which is why the United States requires savings products to advertise an annual percentage yield rather than a nominal rate, and why Australia and the United Kingdom use comparison rates and annual equivalent rates for the same purpose.
This converter puts any quote onto the effective basis so you are comparing like with like, and shows the premium in both percentage points and dollars so you can judge whether the difference is worth acting on or is small enough to ignore.
How to use it
- Enter the nominal annual rate exactly as the product discloses it, which is the large number in the advertisement or the rate named in the terms and conditions, and enter it as a percentage rather than a decimal.
- Then choose the compounding frequency, which is stated in the terms under a heading such as how interest is calculated and paid: savings accounts are usually monthly, term deposits can be annual or at maturity, credit cards are typically daily, and mortgages are usually monthly.
- Choose continuous only if you are working with a pricing model, since no retail product actually compounds continuously.
- Finally enter an example balance so the difference is shown in dollars as well as percentage points, because a two hundredths of a percentage point gap reads very differently on a thousand dollars than on a million.
What each result means
- Effective annual rate (APY)
- What the product really returns or costs over a year once interest earned on interest is counted. Use this to compare offers.
- Nominal annual rate (APR)
- The headline rate as quoted, which ignores compounding within the year and is therefore not directly comparable between products.
- Compounding frequency
- How often interest is added to the balance. More frequent compounding raises the effective rate for the same nominal figure.
- Rate per compounding period
- The nominal rate divided by the number of periods, which is the rate actually applied at each compounding event.
- Interest in one year on the example balance
- The dollar effect of the effective rate, assuming no deposits or withdrawals and all interest left in place.
- Balance after one year
- Opening balance plus one year of compounded interest, before any fees, tax or withholding is applied.
- Difference between APY and APR
- The compounding premium in percentage points. It widens as either the rate or the compounding frequency increases.
The formula
Effective annual rate = the quantity one plus the nominal annual rate divided by the number of compounding periods per year, raised to the power of the number of periods per year, minus one
Written out: APY equals (1 + APR / n) to the power n, minus 1, where APR is the nominal annual rate expressed as a decimal and n is the number of compounding periods in a year. For continuous compounding the limit as n grows without bound is the exponential of the nominal rate minus one. The rate per compounding period is simply the nominal annual rate divided by n. Interest over one year in dollars equals the balance multiplied by the effective annual rate.
How this number is used in practice
The gap matters most where rates are high. At 3 per cent nominal, moving from annual to daily compounding adds under five hundredths of a percentage point, which on a typical savings balance is a rounding error. At 20 per cent, the same change adds more than two full percentage points, which is why credit card interest compounds faster than people expect.
That asymmetry is the practical rule to carry away: chase compounding frequency on debt, not on deposits. If you are choosing between savings accounts, the headline rate and the fees will dominate the frequency almost every time; if you are carrying card debt, the daily compounding is a real and substantial part of what you are paying.
Watch out for what the acronym is actually describing in your country, because the terms are not used consistently. In the United States, annual percentage yield is a regulated term for deposits and always includes compounding, while annual percentage rate on loans includes certain fees but is quoted as a nominal rate.
In the United Kingdom, savings use annual equivalent rate, which is an effective rate. In Australia, credit products must show a comparison rate that folds in most fees and charges, which is a different adjustment again and is not the same thing as an effective annual rate.
Converting a nominal rate to an effective one, as this tool does, never substitutes for a comparison rate, because fees are not part of the calculation at all.
Finally, remember that the effective rate assumes interest is left to compound. A savings account where you sweep the interest out each month to spend it returns the nominal rate, not the effective one, because nothing is compounding. The same is true of an income-focused term deposit paying interest to a separate transaction account. If you want the effective rate the advertisement implies, the interest has to stay where it was earned.
Worked examples
5 per cent nominal compounded monthly on a 10,000 dollar balance
Effective rate of 5.1162 per cent, 511.62 dollars of interest and a premium of 0.1162 percentage points over the headline
5 per cent nominal compounded annually on the same balance
Effective rate stays at 5.0000 per cent and interest is exactly 500.00 dollars with no compounding premium
19.99 per cent credit card rate applied daily on a 5,000 dollar balance
Effective rate of 22.1214 per cent, costing 1,106.07 dollars a year rather than the 999.50 dollars the headline implies
When people use it
- Comparing two savings accounts quoting the same headline rate but compounding differently
- Working out what a credit card's daily periodic rate really costs over a year
- Converting a nominal mortgage rate into the effective rate for a spreadsheet model
- Checking whether a term deposit paying at maturity beats a monthly-paying account
- Teaching the difference between nominal and effective rates in a finance or accounting class
Tips
- The higher the rate, the more compounding frequency matters. It is a rounding error at 3 per cent and worth real money at 20 per cent.
- Always compare products on the effective rate, and if only one of them quotes one, convert the other before deciding.
- Most of the available premium arrives by moving from annual to monthly compounding. Daily against monthly is a very small further step.
- An Australian comparison rate is not an effective annual rate; it includes fees. Do not treat the two as interchangeable.
- Interest you withdraw is interest that does not compound, so sweeping interest out each month returns the nominal rate instead.
- Check the day count convention in the terms. A 360 day year quietly changes the daily rate and the annual result.
What it assumes, and where it stops being accurate
- Ignores fees, account-keeping charges, introductory or bonus rates, minimum balance conditions and tiered rates, all of which usually matter more than the compounding frequency.
- Assumes the rate is constant for a full year. Variable-rate products change, so the effective rate here is a snapshot rather than a forecast.
- Assumes all interest is left in the account to compound. Withdrawing interest as it is paid returns the nominal rate rather than the effective rate.
- Uses a 365 day year for daily compounding. Some products use 360 or 366 days, which changes the result very slightly.
- Not a substitute for a regulated comparison rate or annual percentage rate on credit, since those include fees that this calculation does not.
- Ignores tax entirely. Interest is usually assessable income, so the after-tax effective return is lower than shown here.
Terms used on this page
- Nominal rate
- A quoted annual rate that does not account for compounding within the year, also called the stated or headline rate.
- Effective annual rate
- The rate that would produce the same result over a year if interest compounded only once, making products comparable.
- Compounding period
- The interval at which accrued interest is added to the balance and begins earning interest itself.
- Periodic rate
- The nominal annual rate divided by the number of compounding periods, applied at each compounding event.
- Comparison rate
- An Australian regulated figure for credit products that includes most fees as well as interest, not the same as an effective rate.
Questions people ask
- What is the difference between APR and APY?
- APR is a nominal annual rate that does not account for compounding within the year, while APY, also called the effective annual rate, folds compounding in so products with different schedules can be compared directly. For the same product, APY is always equal to or higher than APR, and they are only equal when compounding is annual.
- Does more frequent compounding always give a higher return?
- For a positive nominal rate, yes, but with rapidly diminishing returns. Each increase in frequency adds less than the one before, and the sequence converges on continuous compounding as a ceiling. At typical savings rates the difference between daily and monthly compounding is a few hundredths of a percentage point.
- Can I convert an APY back to an APR?
- Yes, by rearranging the same formula. The nominal rate equals the number of periods multiplied by the quantity one plus the effective rate raised to the power of one over the number of periods, minus one. You need to know the compounding frequency to do it, since the same effective rate maps to different nominal rates at different frequencies.
- Why do credit cards cost more than the quoted rate?
- Most cards convert the annual rate into a daily periodic rate and apply it to the balance every day, so interest compounds daily. On a 20 per cent nominal rate that lifts the effective cost above 22 per cent. Cash advances usually attract a higher rate with no interest-free period, which widens the gap further.
- Is continuous compounding used by real products?
- No retail savings or lending product compounds continuously. It is a mathematical limit used in option pricing, bond mathematics and academic finance because it makes the algebra cleaner. It is included here to show the ceiling, and the difference between daily and continuous compounding is negligible at ordinary rates.
- Does this account for fees?
- No. It converts rates only. Account-keeping fees, establishment fees, monthly service charges and early withdrawal penalties can easily outweigh any difference in compounding frequency, which is why regulators require fee-inclusive figures such as the Australian comparison rate for credit products.
Use this with
APR to APY Converter answers one part of the question. These pick up where it stops: Compound Interest Calculator, Simple Interest Calculator, Savings Goal Calculator, Credit Card Payoff Calculator and CD Ladder Calculator.
Where these figures come from
This calculation is jurisdiction-neutral arithmetic. No country-specific rules are applied.
- Consumer Financial Protection Bureau: Regulation DD, Truth in Savings. The United States rules defining annual percentage yield for deposit accounts
- ASIC Moneysmart. Australian guidance on comparison rates, compound interest and savings products
- Federal Deposit Insurance Corporation. Consumer guidance on deposit account disclosures and yields
APR to APY Converter produces an estimate for general information. It is not financial, tax, medical, legal or engineering advice. read the full disclaimer. Spotted a wrong number? Report it and it gets fixed. The form picks up this calculator and the inputs you used.