What is the difference between APR and APY?

A nominal annual rate ignores compounding; APY is the effective annual yield and includes it. A 5% nominal rate compounded monthly earns about 5.116% over a year because interest itself earns interest. The APR / nominal label in this tool means the supplied nominal rate. Regulated loan APR can include fees and disclosure rules that this formula does not calculate.

How is APY calculated?

APY = (1 + r/n)^n − 1, where r is the nominal annual rate as a decimal and n is the number of compounding periods per year. For 5% compounded monthly: (1 + 0.05/12)^12 − 1 = 0.05116, or 5.116%. For continuous compounding the limit is e^r − 1. The tool prints the substituted formula alongside the answer.

Does compounding more often always earn more?

For a positive nominal rate and at least one compounding period per year, more frequent compounding raises the effective yield with diminishing returns. At 5% nominal: annual APY is 5%, monthly about 5.116%, daily about 5.127%, and continuous about 5.127%. An already effective APY is not compounded a second time: 5% APY on 1,000 earns 50 over one year without deposits.

Can I work backwards from an advertised APY?

Yes. The reverse mode solves for the nominal rate: r = n × ((1 + APY)^(1/n) − 1). This is the useful direction when comparing an account advertising 4.5% APY compounded daily against one advertising a 4.45% nominal rate, which are nearly the same product described two ways.

Does it handle negative rates?

Yes. Negative nominal rates compound the same way and the tool computes them rather than erroring, which matters for modelling real-terms returns after inflation or the negative-rate environments some central banks have run. A zero rate returns exactly zero rather than a floating-point artefact near it.

Is this financial advice?

No. This is an arithmetic tool: it computes what a rate does under a compounding schedule you specify, and nothing more. It does not know your tax position, does not model fees, introductory rates or early-withdrawal penalties, and offers no opinion on any product. For decisions about your money, talk to a qualified adviser.

How do I convert APY to monthly or daily interest?

For a supplied APY as a decimal, the equivalent monthly rate is (1 + APY)^(1/12) − 1 and the daily rate uses 365 instead of 12. In APY → rate, choose Monthly or Daily and enter the principal. The result includes Rate per compounding period and Interest for one compounding period on the starting principal. This assumes a fixed opening balance for that period; it does not reproduce changing daily balances or a bank statement.

Is 4% APY paid every month, and is 1% per month 12% per year?

APY is an annual effective yield. A 4% APY has an equivalent monthly rate of about 0.327374%; it does not mean earning 4% each month. A 1% effective monthly rate compounds to about 12.682503% annually, while 12% nominal compounded monthly has the same 1% periodic rate. Actual payment dates belong to the account terms.

How much is 3%, 3.5%, 3.75%, 4.1% or 4.5% APY on 10,000?

Over one year with no deposits or withdrawals and a constant supplied APY, interest is 300, 350, 375, 410 or 450 respectively. In Balance over time choose Effective APY, enter your supplied rate, starting amount and one year. These are arithmetic examples, not current account offers or recommendations about whether a yield is good.

Can I model savings with regular deposits or repeated annual increases?

Balance over time accepts the starting amount, term in years, deposit amount, deposit frequency and whether deposits occur at the start or end of each period. For pure numeric annual growth, choose Effective APY and no deposits: 100 at 3% annually for three years becomes 109.2727. This applies a known rate; it does not solve a CAGR from two endpoints.

Is this the FFIEC APY disclosure calculator?

No. This page applies supplied nominal/effective-rate and balance formulas. It does not verify Truth in Savings disclosures, construct periodic-statement APY earned from historical balances or represent the FFIEC tool. For a certificate maturity amount from a supplied term in months, CD Calculator has that dedicated workflow.

APY & Interest Calculator

Convert a supplied nominal annual rate to APY, work backwards from an advertised APY, or calculate a balance over time with optional regular deposits. In Balance over time, choose whether the rate you have is nominal or an effective APY. Both rate forms, equivalent per-period rates and the arithmetic used are shown; no current account rate, fee, tax or bank crediting policy is chosen.

Effective annual yield (APY)5.11619%5% nominal, compounded monthly

Calculate

Nominal rate (%)

Compounding

Principal

Term (years)

What a stated rate is really worth once it compounds.

The workingthe arithmetic in full
APY = (1 + r ÷ n)^n − 1 = (1 + 0.05 ÷ 12)^12 − 1 = 5.11619%
APYwhat the money actually earns
5.11619%
APR / nominalwhat gets advertised
5%
Rate per compounding periodmonthly
0.416667%
Interest for one compounding periodon the starting 10,000.00 only
41.67
Balance after 1 yearon 10,000.00 starting
10,511.62
Interest earned
511.62

Balance and interest shown on 10,000.00 over 1 year.

Nominal rate and APY are not the same number. The nominal rate ignores compounding; APY includes it. A 5% rate compounded monthly yields 5.116%, and compounded daily it yields 5.127%: same stated rate, different money. The APR / nominal label above means a supplied nominal annual rate. Regulated loan APR can include fees and disclosure rules that this formula does not calculate. Everything on this page is supplied-rate arithmetic.

Common questions

What is the difference between APR and APY?: A nominal annual rate ignores compounding; APY is the effective annual yield and includes it. A 5% nominal rate compounded monthly earns about 5.116% over a year because interest itself earns interest. The APR / nominal label in this tool means the supplied nominal rate. Regulated loan APR can include fees and disclosure rules that this formula does not calculate.
How is APY calculated?: APY = (1 + r/n)^n − 1, where r is the nominal annual rate as a decimal and n is the number of compounding periods per year. For 5% compounded monthly: (1 + 0.05/12)^12 − 1 = 0.05116, or 5.116%. For continuous compounding the limit is e^r − 1. The tool prints the substituted formula alongside the answer.
Does compounding more often always earn more?: For a positive nominal rate and at least one compounding period per year, more frequent compounding raises the effective yield with diminishing returns. At 5% nominal: annual APY is 5%, monthly about 5.116%, daily about 5.127%, and continuous about 5.127%. An already effective APY is not compounded a second time: 5% APY on 1,000 earns 50 over one year without deposits.
Can I work backwards from an advertised APY?: Yes. The reverse mode solves for the nominal rate: r = n × ((1 + APY)^(1/n) − 1). This is the useful direction when comparing an account advertising 4.5% APY compounded daily against one advertising a 4.45% nominal rate, which are nearly the same product described two ways.
Does it handle negative rates?: Yes. Negative nominal rates compound the same way and the tool computes them rather than erroring, which matters for modelling real-terms returns after inflation or the negative-rate environments some central banks have run. A zero rate returns exactly zero rather than a floating-point artefact near it.
Is this financial advice?: No. This is an arithmetic tool: it computes what a rate does under a compounding schedule you specify, and nothing more. It does not know your tax position, does not model fees, introductory rates or early-withdrawal penalties, and offers no opinion on any product. For decisions about your money, talk to a qualified adviser.
How do I convert APY to monthly or daily interest?: For a supplied APY as a decimal, the equivalent monthly rate is (1 + APY)^(1/12) − 1 and the daily rate uses 365 instead of 12. In APY → rate, choose Monthly or Daily and enter the principal. The result includes Rate per compounding period and Interest for one compounding period on the starting principal. This assumes a fixed opening balance for that period; it does not reproduce changing daily balances or a bank statement.
Is 4% APY paid every month, and is 1% per month 12% per year?: APY is an annual effective yield. A 4% APY has an equivalent monthly rate of about 0.327374%; it does not mean earning 4% each month. A 1% effective monthly rate compounds to about 12.682503% annually, while 12% nominal compounded monthly has the same 1% periodic rate. Actual payment dates belong to the account terms.
How much is 3%, 3.5%, 3.75%, 4.1% or 4.5% APY on 10,000?: Over one year with no deposits or withdrawals and a constant supplied APY, interest is 300, 350, 375, 410 or 450 respectively. In Balance over time choose Effective APY, enter your supplied rate, starting amount and one year. These are arithmetic examples, not current account offers or recommendations about whether a yield is good.
Can I model savings with regular deposits or repeated annual increases?: Balance over time accepts the starting amount, term in years, deposit amount, deposit frequency and whether deposits occur at the start or end of each period. For pure numeric annual growth, choose Effective APY and no deposits: 100 at 3% annually for three years becomes 109.2727. This applies a known rate; it does not solve a CAGR from two endpoints.
Is this the FFIEC APY disclosure calculator?: No. This page applies supplied nominal/effective-rate and balance formulas. It does not verify Truth in Savings disclosures, construct periodic-statement APY earned from historical balances or represent the FFIEC tool. For a certificate maturity amount from a supplied term in months, CD Calculator has that dedicated workflow.

Browser double-precision arithmetic, rounded to about fifteen significant digits before display. Compounding uses the supplied convention; bank fees, tax, tiered rates and actual crediting policies are not modelled.