APY Calculator — Annual Percentage Yield from Any Rate

How to use the APY calculator

1. Choose what to Calculate: APY from a rate, Rate from an APY or APY from interest earned.
2. For a rate or an APY, enter the number, then pick the Compounding that the account uses (yearly, half-yearly, quarterly, monthly, daily or continuous).
3. Optionally enter a Deposit to see the interest it would earn in one year.
4. For APY from interest earned, enter the Amount deposited, the Interest earned and the Days in the term from your statement or CD disclosure.
5. Read the APY (rounded to two decimals, and with more decimals below it). The table shows what the same rate would yield at every compounding frequency.

What it does and when to use it

Banks advertise savings accounts, money market accounts and certificates of deposit by their APY. Sometimes you only have the nominal rate, such as a rate in an account agreement, a rate from another country, or a bond coupon. Sometimes you have the APY but need the rate behind it. And sometimes you want to check what an account really paid.

This calculator handles all three:

• Comparing offers fairly. One account says “4.50% compounded daily” and another says “4.60% APY”. Converting both to APY puts them on the same footing.
• Working backwards. If a CD advertises a 5% APY with daily compounding, the nominal rate is about 4.879%.
• Checking a statement. If a 182-day CD paid $30.37 on $1,000, the annualized yield is 6.18%.
• Seeing a year’s interest on a deposit before you move money.

How it works

APY from a nominal rate. With a yearly rate r (as a decimal) compounded n times a year:

APY = (1 + r ÷ n)^n − 1

For continuous compounding, APY = e^r − 1, where e is about 2.71828.

Rate from an APY. The tool reverses the formula: r = n × ((1 + APY)^(1 ÷ n) − 1), or r = ln(1 + APY) for continuous compounding.

APY from interest earned (Regulation DD). US deposit accounts must disclose APY using the Truth in Savings rules. Appendix A to Regulation DD gives the general formula:

APY = 100 × [(1 + interest ÷ principal)^(365 ÷ days in term) − 1]

When the term is exactly 365 days, this becomes APY = 100 × (interest ÷ principal). The formula takes interest actually earned over any term and turns it into a yearly rate, with compounding included.

Interest in one year is the deposit × APY, which assumes the rate stays fixed and the interest stays in the account.

Worked examples

These examples were calculated by this tool. The first two match the worked examples in Regulation DD Appendix A.

1. 6% compounded monthly. (1 + 0.06 ÷ 12)^12 − 1 = 0.061678, so the APY is 6.17%. On $1,000 that is $61.68 of interest in one year. Regulation DD uses this same $61.68 on $1,000 over 365 days as its example of a 6.17% APY.

2. A six-month CD. A $1,000 certificate pays $30.37 over 182 days. The return over the term is 3.037%. Annualized with the Regulation DD formula, (1.03037)^(365 ÷ 182) − 1 gives an APY of 6.18%, as in the regulation’s example.

3. Rate behind an advertised APY. A 5% APY with daily compounding needs a nominal rate of 4.879%. With monthly compounding, the same 4.879% would only reach 4.99%, or $499.00 on $10,000 instead of $500.00.

4. A 4.5% savings rate compounded daily. The APY is 4.6025%, which rounds to 4.6%. On $10,000 that is $460.25 of interest in one year, compared with $450.00 if interest were paid once a year.

How much compounding adds at 6%

The jump from yearly to monthly is worth $1.68 per $1,000. Going from monthly to daily adds about 15 cents more. So a small difference in the rate usually matters more than the compounding frequency.

Comparing two accounts

Say Bank A offers 4.50% compounded daily and Bank B offers a 4.60% APY. Enter 4.5 with daily compounding: the APY is 4.6025%. On $10,000, Bank A pays $460.25 in a year and Bank B pays $460.00. The gap is tiny, so other details may matter more: fees, minimum balances, how easily you can withdraw, and how long the rate is promised. The point is that a rate and an APY cannot be compared until both are in the same terms.

Limits and tips

• The rate is assumed fixed for a year. Variable savings rates can change at any time.
• Daily compounding uses 365 days. Some products may use a 360-day year for daily rates. That changes the result very slightly.
• Balances are assumed to stay put. Deposits, withdrawals, fees and minimum balance rules change what you really earn.
• APY is before tax. Interest is generally taxable in the US.
• Rounding. The headline APY is rounded to two decimals. Use the more precise figure when you are checking a calculation to the cent.

Related calculators

• See what regular deposits grow to over many years with the compound interest calculator.
• Convert any nominal rate in any currency with the effective annual rate calculator, or compare growth with and without compounding in the simple vs compound interest calculator.
• See the flip side of compounding on debt with the credit card interest calculator.