How to use this APY calculator
- Pick what you want to find. “Rate → APY” converts an interest rate into a yield, “APY → rate” goes the other way, and “Earnings” projects a balance over time.
- Enter the rate and how often it compounds. Your account disclosure states the compounding frequency. If you start from an APY, the frequency changes the interest rate shown but not the APY.
- Add your deposit to see the interest it earns in one year at that yield.
- In Earnings mode, set a monthly deposit and a time period. Under “Taxes & inflation” you can enter your tax rate and an inflation rate. Use “Copy link” to save the scenario.
What is APY, and how is it different from APR?
A deposit account has two rates. The interest rate is the yearly rate the bank pays before compounding. The annual percentage yield (APY) is what the account earns over a year once interest is added to the balance and starts earning interest of its own. Regulation DD, the federal rule behind the Truth in Savings Act, defines the interest rate as “the annual rate of interest paid on an account which does not reflect compounding,” and the APY as a rate reflecting “the total amount of interest paid on an account, based on the interest rate and the frequency of compounding for a 365-day period” (§ 1030.2).
That is why savers sometimes see “APR” on a savings account: for account disclosures the rule lets the interest rate also be called the “annual percentage rate.” Banks must disclose both the APY and the interest rate, and how often interest is compounded and credited (§ 1030.4). If an advertisement states a rate of return, it has to be the APY; the interest rate may appear next to it, but not more prominently (§ 1030.8).
Do not mix this up with a loan APR. For a mortgage, the CFPB explains that the APR is a broader measure of borrowing cost than the interest rate, because it adds points, broker fees and other charges. On a plain deposit account the gap between the two rates comes from compounding. This calculator uses “interest rate (APR)” in the deposit sense.
How is APY calculated? The formula
To convert an interest rate to an APY, compound the rate over the year and subtract the original 1:
APY = (1 + r ÷ n)^n − 1
- APY
- annual percentage yield, as a decimal
- r
- interest rate (APR) as a decimal, before compounding
- n
- compounding periods per year: 365 daily, 52 weekly, 12 monthly, 4 quarterly, 2 semiannual, 1 annual
Worked example
Take a 4% interest rate compounded daily. Then r ÷ n = 0.04 ÷ 365 = 0.000109589, and (1 + 0.000109589)365 = 1.040808. So APY = 1.040808 − 1 = 4.081%. On $10,000, that is $408.08 of interest in a year, compared with $400 if the interest never compounded. Compounded monthly, the same rate gives 4.074%; compounded once a year it gives 4%, the same as the rate. With continuous compounding the formula becomes APY = er − 1 = 4.081%.
How banks calculate it
A bank does not start from the interest rate. Regulation DD Appendix A defines the APY from the dollars of interest an account earns, using the actual number of days in the term and a 365-day year (Appendix A):
APY = 100 × [(1 + Interest ÷ Principal)^(365 ÷ Days in term) − 1]
- Principal
- the amount assumed to be deposited at the start
- Interest
- total dollars of interest earned on that principal over the term
- Days in term
- actual days in the term of the account (365 for an account with no stated maturity)
The appendix works its own example: a six-month certificate of deposit of 182 days that pays $30.37 on $1,000 has an APY of 100 × [(1 + 30.37 ÷ 1,000)365 ÷ 182 − 1] = 6.18%. For a 365-day term the formula collapses to Interest ÷ Principal, so the $408.08 earned on $10,000 in the example above gives 4.081% again. The formula assumes all principal and interest stay on deposit for the term and that no other deposits or withdrawals occur. Banks state the result to the nearest 0.01 percentage point (§ 1030.3), which is why this calculator also shows the rounded figure.
APR to APY conversion table
The APY produced by each interest rate at each compounding frequency, worked out with the formula above:
| Interest rate | Continuously | Daily | Monthly | Quarterly | Semiannually | Annually |
|---|---|---|---|---|---|---|
| 1.00% | 1.005% | 1.005% | 1.005% | 1.004% | 1.002% | 1.000% |
| 2.00% | 2.020% | 2.020% | 2.018% | 2.015% | 2.010% | 2.000% |
| 3.00% | 3.045% | 3.045% | 3.042% | 3.034% | 3.022% | 3.000% |
| 4.00% | 4.081% | 4.081% | 4.074% | 4.060% | 4.040% | 4.000% |
| 5.00% | 5.127% | 5.127% | 5.116% | 5.095% | 5.062% | 5.000% |
| 6.00% | 6.184% | 6.183% | 6.168% | 6.136% | 6.090% | 6.000% |
Reading across a row, compounding becomes less frequent and the APY falls until it equals the interest rate at annual compounding; continuous compounding, the theoretical limit, gives the highest APY. Reading down a column, the gap between the interest rate and the APY widens as the rate goes up: at 1% daily compounding adds 0.005 percentage points, at 6% it adds 0.183.
How to convert APY to APR (interest rate)
Solving the same formula for r gives the interest rate that produces a given APY:
r = n × [(1 + APY)^(1/n) − 1]
- r
- interest rate (APR) as a decimal, before compounding
- APY
- annual percentage yield, as a decimal
- n
- compounding periods per year (for continuous compounding use r = ln(1 + APY))
For a 4% APY compounded daily, (1 + 0.04)1/365 = 1.00010746, so r = 365 × (1.00010746 − 1) = 3.922%. The same APY needs a 3.928% rate compounded monthly, 3.941% compounded quarterly and 4% compounded annually. The more often interest compounds, the lower the interest rate needs to be to deliver the same APY.
| APY | Daily | Monthly | Quarterly | Annually |
|---|---|---|---|---|
| 3.00% | 2.956% | 2.960% | 2.967% | 3.000% |
| 4.00% | 3.922% | 3.928% | 3.941% | 4.000% |
| 4.50% | 4.402% | 4.410% | 4.426% | 4.500% |
| 5.00% | 4.879% | 4.889% | 4.909% | 5.000% |
Does compounding frequency matter?
Yes, but by less than the rate does. Banks accrue interest every day, using a daily rate of at least 1/365 of the interest rate, and the rule does not require them to compound or credit it at any particular frequency (§ 1030.7). Here is $10,000 at a 4% interest rate under each schedule, with no deposits or withdrawals:
| Compounding | APY | Interest after 1 year | Interest after 5 years | Interest after 10 years |
|---|---|---|---|---|
| Daily | 4.081% | $408.08 | $2,213.89 | $4,917.92 |
| Weekly | 4.079% | $407.95 | $2,213.09 | $4,915.95 |
| Monthly | 4.074% | $407.42 | $2,209.97 | $4,908.33 |
| Quarterly | 4.060% | $406.04 | $2,201.90 | $4,888.64 |
| Semiannually | 4.040% | $404.00 | $2,189.94 | $4,859.47 |
| Annually | 4.000% | $400.00 | $2,166.53 | $4,802.44 |
| Continuously | 4.081% | $408.11 | $2,214.03 | $4,918.25 |
Daily instead of monthly compounding adds $3.93 over 5 years on $10,000. Daily instead of annual compounding adds $8.08 in the first year and $47.36 over 5 years. For comparison, the difference between earning 0.37% and 4.00% on the same $10,000 is $363.00 in a single year (see below). When you compare accounts, compare their APYs; the APY already contains the compounding.
What is a good APY?
It depends on the type of account and the date, so measure an offer against a few benchmarks. The FDIC’s national savings rate was 0.37% in its September 21, 2026 update, which the FDIC bases on data from the end of the previous month. The FDIC describes its national rate as the average of rates paid by all insured banks and credit unions for which data is available, weighted by each institution’s share of domestic deposits (FDIC national rates). The FDIC does not say whether that figure is an interest rate or an APY; at this level the two differ by only 0.0007 percentage points, so the table below treats it as an APY.
Among the best online high-yield savings accounts on Bankrate’s list, advertised APYs were roughly 4.00% or a little higher as of September 28, 2026. That is an example of what the best advertised accounts pay, not an average, and advertised rates can change at any time. It is about 11 times the national average.
| Scenario | Interest at 0.37% (FDIC average) | Interest at 4.00% (high-yield example) | Difference |
|---|---|---|---|
| $10,000 for 1 year | $37.00 | $400.00 | $363.00 |
| $10,000 for 5 years | $186.37 | $2,166.53 | $1,980.15 |
| $10,000 plus $200 a month for 5 years | $295.99 | $3,402.33 | $3,106.34 |
Inflation is the other benchmark. Consumer prices rose 3.4% in the 12 months through August 2026 (BLS CPI-U). A 4.00% APY against 3.4% inflation leaves a yield after inflation of about 0.58% before taxes; the 0.37% national average falls well behind prices. An APY below the inflation rate grows your balance more slowly than prices rise.
How much interest does $10,000 earn at different APYs?
Interest earned by $10,000 left in an account with no deposits or withdrawals, before taxes, at a constant APY:
| APY | 1 year | 3 years | 5 years |
|---|---|---|---|
| 0.50% | $50.00 | $150.75 | $252.51 |
| 1.00% | $100.00 | $303.01 | $510.10 |
| 2.00% | $200.00 | $612.08 | $1,040.81 |
| 3.00% | $300.00 | $927.27 | $1,592.74 |
| 4.00% | $400.00 | $1,248.64 | $2,166.53 |
| 5.00% | $500.00 | $1,576.25 | $2,762.82 |
The “Earnings” mode adds monthly deposits. Starting with $10,000 and adding $200 at the end of every month at a 4% APY builds $25,402.33 in 5 years: $22,000 of deposits plus $3,402.33 of interest. At a 24% tax rate the interest falls to $2,532.54, because tax is taken out as interest is earned and the smaller balance compounds more slowly.
APY on a CD or a savings account
The APY is the same idea on any deposit account, but a few rules of the definition matter when you rely on it:
- It assumes the interest stays put. Appendix A bases the APY on all principal and interest remaining on deposit for the term. For a CD that compounds and lets you withdraw interest before maturity, the bank must state that the APY assumes interest remains on deposit and that a withdrawal will reduce earnings (§ 1030.4). Use the CD calculator for terms, taxes and early-withdrawal penalties.
- It can change on a savings account. An advertisement that states an APY generally must say how long the APY will be offered or the date it is accurate as of, and, for a variable-rate account, that the rate may change after the account is opened (§ 1030.8). Check the current APY before you rely on a projection.
- Fees and balance minimums count. An advertisement that states an APY generally must give the minimum balance needed to earn it and say that fees could reduce earnings. This calculator does not model either.
- Bonuses are separate. The APY reflects only interest, not the value of a bonus for opening, maintaining or increasing an account (Appendix A).
Deposits at an FDIC-insured bank are covered up to $250,000 per depositor, per insured bank, for each account ownership category. Interest is also taxable: the IRS treats most bank interest as income in the year it becomes available to you and requires you to report it even without a Form 1099-INT (IRS Topic 403).
What this calculator does not model
- It assumes a constant rate. Savings account rates can change; CD rates are fixed for the term.
- Monthly deposits arrive at the end of each month, and there are no withdrawals. A deposit made earlier in the month would earn slightly more.
- Daily compounding uses 365 periods a year, the 365-day basis of Regulation DD; leap years are ignored.
- Tax is a single flat rate applied to interest as it is earned. It does not calculate your actual tax bill.
- Fees, tiered rates, balance minimums and bonuses are not included.
For a savings goal or the time to reach one, use the savings calculator. For annual deposits, simple versus compound interest and a monthly schedule, use the interest calculator. For long-term growth with different returns, see the compound interest calculator, and for interest that is never reinvested, the simple interest calculator. To see what your balance will buy in the future, try the inflation calculator.
Frequently asked questions
How do you convert APR to APY?
Use APY = (1 + r ÷ n)n − 1, where r is the interest rate as a decimal and n is the number of compounding periods a year. A 4% rate compounded daily gives (1 + 0.04 ÷ 365)365 − 1 = 4.081%; compounded monthly it is 4.074%. With annual compounding the APY equals the rate.
How do you convert APY to APR (interest rate)?
Use r = n × [(1 + APY)1/n − 1], where n is the number of compounding periods a year. A 4% APY compounded daily comes from a 3.922% interest rate, compounded monthly from 3.928%, and compounded annually from 4%. For continuous compounding the rate is ln(1 + APY) = 3.922%.
What is the difference between APY and APR on a savings account?
APY includes the effect of compounding; the interest rate, which banks sometimes label APR, does not. Regulation DD defines the interest rate as the annual rate paid “which does not reflect compounding” and requires banks to disclose both figures and to state any advertised return as an APY. On a mortgage, the APR is a different, broader measure that also counts fees.
Does compounding frequency matter?
It matters, but far less than the rate itself. A 4% interest rate on $10,000 earns $2,213.89 over 5 years compounded daily, $2,209.97 compounded monthly and $2,166.53 compounded annually. Daily instead of monthly adds only $3.93. Comparing accounts by APY already accounts for compounding.
What is a good APY?
There is no single number, so compare an account with benchmarks. The FDIC’s national savings rate was 0.37% in its September 21, 2026 update. Among the best online high-yield accounts, advertised APYs were roughly 4.00% or a little higher as of September 28, 2026, an example of top advertised rates rather than an average. Consumer prices rose 3.4% in the 12 months through August 2026. Fees and minimum balances also matter.
How do banks calculate APY?
Banks use the formula in Regulation DD Appendix A: APY = 100 × [(1 + Interest ÷ Principal)365 ÷ Days in term − 1], with the actual number of days in the term. The calculation assumes all principal and interest stay on deposit, and accounts with no stated maturity use a 365-day term. Banks state the result to the nearest 0.01 percentage point.
How much interest will $10,000 earn at a 4% APY?
By definition, $10,000 at a 4% APY earns $400.00 in a year if it stays in the account and the rate does not change. After 5 years with no deposits it grows to $12,166.53, which is $2,166.53 of interest. Adding $200 a month at the end of each month raises the 5-year balance to $25,402.33.
Is the interest I earn taxable?
Yes. The IRS says most interest credited to an account you can withdraw from without penalty is taxable in the year it becomes available, and you should receive a Form 1099-INT if you were paid $10 or more in interest. At a 24% tax rate, the $2,166.53 of 5-year interest on $10,000 at a 4% APY leaves about $1,607.86 after tax, because tax also slows compounding.