APY Calculator
APY Calculator
Turn an interest rate into the annual percentage yield it really earns, or turn an APY back into the rate behind it, for any compounding from yearly to daily and continuous. See the interest a deposit earns and how much the compounding adds.
APY by compounding
APY = (1 + r ÷ n) to the power n − 1, where r is the yearly interest rate and n the number of compounding periods a year; continuous compounding gives e to the power r − 1. Going the other way, r = n × ((1 + APY) to the power 1 ÷ n − 1). Interest on a deposit = deposit × ((1 + r ÷ n) to the power n × years − 1). Daily compounding uses a 365 day year. The CSV, image and printed report contain the values you entered, nothing preloaded.
How to use this tool
Enter an interest rate and choose how often it compounds, and the calculator shows the annual percentage yield, the APY, with the extra the compounding adds. Switch the first box to start from an APY and it finds the rate behind it. Add a deposit and a number of months to see the interest it earns, the balance at the end and how that compares with simple interest.
The setting people most often get wrong is the compounding. A savings account usually compounds daily or monthly, a certificate of deposit may compound daily or quarterly, and the account terms will say which. If a bank already quotes an APY, compare that number directly; it has the compounding built in.
What the calculation is doing
A quoted interest rate is split across the compounding periods: 5% compounded daily pays 5% ÷ 365 = 0.0137% each day. Each day's interest is added to the balance and earns interest from then on, so after a year the balance has grown by (1 + 0.05 ÷ 365) to the power 365 − 1 = 5.1267%. That yearly growth is the APY.
The more often interest compounds, the higher the APY, but the gain shrinks with each step. The limit, continuous compounding, gives e to the power of the rate minus 1, 5.1271% for 5%. Going the other way, an APY can be turned back into the rate that produces it for any compounding, which is handy when comparing an account quoted as an APY with a loan quoted as a rate.
APY for savings, APR for loans
In the United States the Truth in Savings Act requires banks to quote deposit accounts as an APY, worked out the same way for everyone, so two accounts can be compared directly whatever their compounding. The regulation's own example is $1,000 earning $61.68 in a year, an APY of 6.17%, which is exactly 6% compounded monthly.
Loans work the other way. The Truth in Lending Act requires an APR, which includes certain fees but is not compounded, so it understates the effective cost when interest is charged daily and left unpaid. A credit card at 22% APR compounds to about 24.6% a year on a balance that is never paid down. That is why the same product can look cheaper as a loan and more rewarding as a deposit: the two are quoted on different bases.
At low rates the gap between the two is small: 0.13 of a point at 5% compounded daily. It grows roughly with the square of the rate, which is why compounding matters little for savings accounts but a lot for high rate debt.
APY for common rates
The annual percentage yield for each interest rate and compounding frequency. Daily compounding uses a 365 day year.
| Interest rate | Yearly | Quarterly | Monthly | Daily | Continuous |
|---|---|---|---|---|---|
| 1% | 1% | 1.004% | 1.005% | 1.005% | 1.005% |
| 2% | 2% | 2.015% | 2.018% | 2.02% | 2.02% |
| 3% | 3% | 3.034% | 3.042% | 3.045% | 3.045% |
| 4% | 4% | 4.06% | 4.074% | 4.081% | 4.081% |
| 5% | 5% | 5.095% | 5.116% | 5.127% | 5.127% |
| 6% | 6% | 6.136% | 6.168% | 6.183% | 6.184% |
| 8% | 8% | 8.243% | 8.3% | 8.328% | 8.329% |
| 10% | 10% | 10.381% | 10.471% | 10.516% | 10.517% |
| 15% | 15% | 15.865% | 16.075% | 16.18% | 16.183% |
| 20% | 20% | 21.551% | 21.939% | 22.134% | 22.14% |
| 25% | 25% | 27.443% | 28.073% | 28.392% | 28.403% |
A worked example you can check on paper
A savings account pays 5% compounded daily. The daily rate is 0.05 ÷ 365 = 0.00013699. Raising 1.00013699 to the power 365 gives 1.0512675, so the APY is 5.1267%. On a $10,000 deposit left for a year, the interest is $512.67, compared with $500 at simple interest.
Now the regulation's example: 6% compounded monthly. The monthly rate is 0.5%, and 1.005 to the power 12 = 1.0616778, an APY of 6.1678%. $1,000 earns $61.68 in a year, which rounds to the 6.17% the rule quotes.
Going backward, an account advertising a 5% APY with monthly compounding has a rate of 12 × (1.05 to the power 1 ÷ 12 − 1) = 12 × 0.0040741 = 4.8889%.
Mistakes that catch people out
Comparing a rate with an APY. A 5% rate compounded daily beats a 5% APY. Convert both to APY before choosing.
Expecting daily compounding to transform returns. The difference between monthly and daily is a few dollars a year on typical balances. Chase the higher rate, not the more frequent compounding.
Forgetting that the rate can change. Savings account rates are variable, and introductory rates end. The APY holds only while the rate does.
Treating a card APR as the full cost. Interest compounds daily on unpaid balances, so the effective cost is higher than the APR.
Ignoring tax and inflation. Interest is usually taxable, and a 4% APY in a year of 3% inflation grows buying power by only about 1%.
Popular calculations
Each opens the calculator with those values filled in, and they can be changed once it is open.
Savings rates compounded daily
Rates compounded monthly
Credit card APR compounded daily
APY back to an interest rate
Interest on a deposit
How this was checked
The APY formula was checked against the example in Appendix A of Regulation DD, the Truth in Savings rules, where $1,000 earning $61.68 in a year is an APY of 6.17%, the result of 6% compounded monthly. Each conversion was checked in both directions, rate to APY and back, and the continuous case was checked as the limit that daily compounding approaches. Deposit balances were checked against the compound interest formula.
Every address in the lists above was then opened and checked for a distinct title, the right APY or rate, a chart that renders, and clean CSV, image and print output containing only the values entered, at desktop, tablet and phone widths.
Common questions
What is the difference between APR and APY?
The interest rate, or APR, is the yearly rate before compounding. The APY is what you actually earn over a year once interest earns interest. At 5% compounded daily the APY is 5.127%. With yearly compounding the two are equal.
How do you calculate APY?
Divide the yearly rate by the number of compounding periods, add 1, raise to the number of periods and subtract 1: APY = (1 + r ÷ n) to the power n − 1. For 6% compounded monthly, (1 + 0.005) to the power 12 − 1 = 6.168%, which is also the example in the US Truth in Savings rules, where $1,000 earns $61.68 in a year.
Does daily compounding make much difference?
Less than people expect. At 5%, going from yearly to monthly adds 0.116 of a point, but from monthly to daily adds only 0.011 more. On $10,000 over 10 years, daily compounding beats monthly by $16.55. The rate itself matters far more than the compounding.
How do I convert APY back to an interest rate?
Reverse the formula: rate = n × ((1 + APY) to the power 1 ÷ n − 1). An APY of 5% with monthly compounding comes from a rate of 4.889%. Choose the APY option in the calculator and pick the compounding.
Why is my credit card costing more than its APR?
Card issuers charge interest daily on the balance, so unpaid interest earns interest too. A 22% APR compounded daily works out to about 24.6% a year if the balance is left to grow. Paying the balance in full each month avoids interest altogether.
Is a higher APY always better?
For savings, yes, if the account is otherwise the same. Check whether the rate is introductory, whether it applies only up to a balance limit, and whether fees or minimum balances would eat into the interest. The APY already reflects compounding, so it is the fair number to compare.
Related Calculators and Reference
- Compound Interest Calculator: grow savings with regular deposits over years.
- Present Value Calculator: discount future money at an effective rate.
- Credit Card Payoff Calculator: what daily compounding costs on a card balance.
- Inflation Calculator: check whether an APY keeps up with prices.
- ROI Calculator: the annualized return on an investment, to compare with a savings APY.
- Savings Goal Calculator: what a savings plan at this yield reaches.
- Rule of 72 Calculator: turn a yield into a doubling time.
- CD Calculator: the interest, APY and maturity value of a certificate of deposit.
- Emergency Fund Calculator: put an APY into an emergency fund and see the time to build it.
- Regulation DD, Appendix A: Annual Percentage Yield Calculation: the US rule for how banks work out the APY.