What is the formula to convert APY to a nominal annual rate?

For n periods per year, nominal rate = n × ((1 + APY)^(1/n) − 1), using APY as a decimal. At 5% APY and n = 12, the nominal annual rate is about 4.888949%. Continuous compounding uses ln(1 + APY).

How do I get monthly or daily interest from APY?

The per-period rate is (1 + APY)^(1/n) − 1. Multiply it by the fixed opening principal to get one period’s interest. Monthly uses n = 12 and Daily uses n = 365 here; those are chosen conventions, not a reconstruction of an account statement.

Can I use 5% APY directly to calculate a year’s interest?

Yes. With a fixed balance of 1,000 for one year, 5% effective APY means 50 interest and a 1,050 ending balance. The nominal-rate figure explains the equivalent compounding rate; it should not replace the APY as if they were the same input.

Does this select a savings account rate or verify a disclosure?

No. Enter the supplied APY and principal. Account rates, fees, tax, tiered balances, payment schedules and FFIEC disclosure verification are outside this formula.

APY to Interest Rate Calculator

Start with the effective annual yield you already have, then select the compounding convention. This page opens on 5% APY, monthly compounding and a starting amount of 1,000: the nominal annual rate is about 4.888949%, the equivalent monthly rate about 0.407412%, and one month’s interest on that fixed opening balance about 4.07. The periodic amount is an arithmetic equivalent; actual bank credit dates and changing balances are separate inputs the tool does not know.

Stated (nominal) rate4.888949%5% effective yield, compounded monthly

Calculate

Effective yield (%)

Compounding

Principal

Term (years)

The stated rate behind an advertised yield.

The workingthe arithmetic in full
r = n × ((1 + APY)^(1÷n) − 1) = 12 × ((1 + 0.05)^(1÷12) − 1) = 4.888949%
APYwhat the money actually earns
5%
APR / nominalwhat gets advertised
4.888949%
Rate per compounding periodmonthly
0.407412%
Interest for one compounding periodon the starting 1,000.00 only
4.07
Balance after 1 yearon 1,000.00 starting
1,050.00
Interest earned
50.00

Balance and interest shown on 1,000.00 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 formula to convert APY to a nominal annual rate?: For n periods per year, nominal rate = n × ((1 + APY)^(1/n) − 1), using APY as a decimal. At 5% APY and n = 12, the nominal annual rate is about 4.888949%. Continuous compounding uses ln(1 + APY).
How do I get monthly or daily interest from APY?: The per-period rate is (1 + APY)^(1/n) − 1. Multiply it by the fixed opening principal to get one period’s interest. Monthly uses n = 12 and Daily uses n = 365 here; those are chosen conventions, not a reconstruction of an account statement.
Can I use 5% APY directly to calculate a year’s interest?: Yes. With a fixed balance of 1,000 for one year, 5% effective APY means 50 interest and a 1,050 ending balance. The nominal-rate figure explains the equivalent compounding rate; it should not replace the APY as if they were the same input.
Does this select a savings account rate or verify a disclosure?: No. Enter the supplied APY and principal. Account rates, fees, tax, tiered balances, payment schedules and FFIEC disclosure verification are outside this formula.

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.