APY Calculator
Effective yearly yield with compounding.
Reviewed by the Calculation Machine team · Updated 24 October 2026 · How we check our maths
Your values
ⓘ Live results
- APY
- 4.594%
- Interest in year 1
- $459.40
- Balance after 1 year
- $10,459.40
- Balance after 5 years
- $12,517.96
Working
- 1APY = (1 + 0.045/12)^12 − 1 = 4.594%
Quick answer
APY (annual percentage yield) is the yearly return after compounding: APY = (1 + r ÷ n)ⁿ − 1, where r is the nominal annual rate and n is the number of compounding periods per year. A 4.5% rate compounded monthly gives an APY of 4.594%, so $10,000 earns $459.40 in a year instead of $450.
What the APY calculator does
This calculator turns a nominal (stated) interest rate into its annual percentage yield for daily, monthly, quarterly or annual compounding, and shows what a starting balance earns after one year and grows to after five.
US banks and credit unions must quote APY on deposit accounts under the Truth in Savings Act, precisely so savers can compare accounts that compound differently. You will mostly need this calculator when a product shows only an interest rate — some CDs, bonds, loans, or rates quoted outside the US — or when you want to check how much compounding frequency is really worth. It also works in reverse for borrowing: a credit card's APR compounded monthly has a higher effective annual cost.
The results assume the rate stays fixed for the whole period and that interest is left in the account to compound. To model regular deposits, use the compound interest calculator; for a fixed-term deposit, the CD calculator includes the term and early-withdrawal effects.
The formula
APY = (1 + r ÷ n)ⁿ − 1 Balance after t years = starting balance × (1 + APY)ᵗ
| Symbol | Meaning | Unit |
|---|---|---|
| r | Nominal annual interest rate as a decimal (4.5% = 0.045) | — |
| n | Compounding periods per year: 365 daily, 12 monthly, 4 quarterly, 1 annually | per year |
| t | Number of years | years |
This is the APY definition in Regulation DD (12 CFR Part 1030), which implements the Truth in Savings Act; Regulation DD's appendix gives an equivalent formula based on the interest actually earned over a term. As n grows without limit the result approaches continuous compounding, APY = eʳ − 1. The same formula converts a loan APR to its effective annual rate (EAR), though a loan's APR also includes some fees.
Worked examples
High-yield savings, daily compounding
A savings account advertises a 5.00% interest rate compounded daily, and you deposit $25,000.
Inputs
- Nominal rate5 %
- CompoundingDaily
- Starting balance25000 $
Result
- APY5.127%
- Interest in year 1$1,281.69
- Balance after 1 year$26,281.69
- Balance after 5 years$32,100.09
The APY is 5.127%, worth $1,281.69 in the first year — about $32 more than simple 5% interest. After five years, with the rate unchanged, the balance would be $32,100.09.
Quarterly-compounding CD
A credit union certificate pays 3.90% compounded quarterly on $5,000.
Inputs
- Nominal rate3.9 %
- CompoundingQuarterly
- Starting balance5000 $
Result
- APY3.957%
- Interest in year 1$197.87
- Balance after 1 year$5,197.87
- Balance after 5 years$6,070.82
The APY is 3.957%. When comparing with a bank CD that quotes APY, use this 3.957% figure, not the 3.90% rate.
Credit card APR as an effective annual rate
A card charges 24% APR with interest compounded monthly, on a $1,000 balance left unpaid for a year.
Inputs
- Nominal rate24 %
- CompoundingMonthly
- Starting balance1000 $
Result
- APY26.824%
- Interest in year 1$268.24
- Balance after 1 year$1,268.24
- Balance after 5 years$3,281.03
The effective annual rate is 26.824%, so $1,000 grows to $1,268.24 if nothing is paid. Compounding works against you on debt as much as it works for you on savings.
How much compounding frequency changes APY
The gain from more frequent compounding is real but small at savings-account rates. Going from monthly to daily adds less than a hundredth of a percentage point at 4.5%; the difference matters more at high rates, such as credit card APRs.
| Compounding | Periods per year | APY | Interest in year 1 |
|---|---|---|---|
| Annually | 1 | 4.500% | $450.00 |
| Quarterly | 4 | 4.577% | $457.65 |
| Monthly | 12 | 4.594% | $459.40 |
| Daily | 365 | 4.602% | $460.25 |
APR vs APY: which number to compare
- APY is used for deposits (savings, money market accounts, CDs). It already includes compounding, so the higher APY earns more, whatever the compounding frequency.
- APR is used for loans and credit cards. It is a nominal yearly rate (plus some fees on loans) and does not include compounding, so the true yearly cost is higher. Enter the APR here with the compounding frequency to see that effective rate.
When comparing two savings accounts, compare APY with APY. When one quotes only a rate, convert it here first. For borrowing costs including fees, see the APR calculator.
Turning APY into real growth
APY tells you one year's growth. Over several years, multiply by (1 + APY) once per year — the five-year balance shown does exactly that. Two things reduce the real result:
- Variable rates: most savings account rates can change at any time, so the five-year figure is only a projection.
- Tax and inflation: interest is usually taxable, and if inflation exceeds your after-tax yield, your purchasing power falls. The inflation calculator shows what a future balance is worth in today's dollars.
How to use the APY Calculator
- 1Enter the nominal annual interest rate from the account terms, for example 4.5.
- 2Choose how often interest compounds: daily, monthly, quarterly or annually. This is listed in the account disclosure.
- 3Enter a starting balance to see the dollar interest; the APY does not depend on the balance.
- 4Read the APY and use it to compare accounts, then check the one-year and five-year balances.
Frequently asked questions
Is APY better than the interest rate?
APY is the more useful number for comparing savings accounts because it includes compounding. It is always equal to or higher than the nominal rate; they match only with annual compounding.
How is interest calculated monthly with APY?
With monthly compounding, each month's interest is the balance × (nominal rate ÷ 12). A $10,000 balance at 4.5% earns $37.50 in the first month, and slightly more each month as interest is added.
What is the difference between daily and monthly compounding?
Very little at typical savings rates. At 4.5%, daily compounding gives 4.602% APY and monthly gives 4.594%, a difference of about $0.85 a year on $10,000.
How do I convert APY back to a nominal rate?
Use r = n × ((1 + APY)^(1/n) − 1). For a 5% APY compounded monthly, r = 12 × (1.05^(1/12) − 1) ≈ 4.889%.
Does APY include fees?
No. APY reflects interest and compounding only. Under Regulation DD, banks disclose an "annual percentage yield earned" on statements, which can be lower if fees were charged.
References
- Regulation DD (Truth in Savings), 12 CFR Part 1030 — Consumer Financial Protection Bureau
- Investments — McGraw Hill (Bodie, Kane and Marcus)
About this calculator
- Built and reviewed by the Calculation Machine team · How we build and test calculators
- Last reviewed: October 24, 2026
- Report an error