APY Calculator
Use this APY calculator to turn a nominal interest rate (APR) into the annual percentage yield your savings account, money market account or CD actually earns, or to work backward from an advertised APY to the underlying rate. Choose how often interest compounds, add a deposit and a term, and you'll see the interest earned, the ending balance and how much compounding adds compared with simple interest.
Updated
Results
- Interest earnedOver the term entered
- Ending balance
- Interest without compoundingFor comparison
| Compounding | APY |
|---|
Results are estimates. See the methodology below.
How to use the calculator
- Pick the direction: APR → APY if you know the interest rate, or APY → APR if you start from an advertised yield.
- Enter the rate.
- Choose the compounding frequency from the account terms: daily, monthly, quarterly, semiannually, annually or continuous.
- Optionally enter a deposit and a term in months (12 by default) to see the interest you'd earn.
The table compares the APY for the same nominal rate under every compounding frequency.
The APY formula
With a nominal annual rate r compounded n times a year:
APY = (1 + r/n)^n − 1
The calculator uses n = 365 for daily, 12 for monthly, 4 for quarterly, 2 for semiannual and 1 for annual compounding. For continuous compounding, APY = e^r − 1. Going the other way, APR = n × ((1 + APY)^(1/n) − 1), or ln(1 + APY) for continuous compounding.
Interest on a deposit D for m months is D × ((1 + APY)^(m/12) − 1). That assumes the rate stays the same, interest stays in the account, and you make no other deposits or withdrawals. Simple interest is D × APR × m/12.
How banks must disclose APY
Under the Truth in Savings Act, implemented by Regulation DD (12 CFR part 1030), banks must disclose the APY so you can compare deposit accounts. Appendix A sets the formula APY = 100 × [(1 + Interest/Principal)^(365/Days in term) − 1], assuming principal and interest stay on deposit for the whole term and no other transactions occur. Accounts with no maturity use an assumed 365-day term.
Worked examples
1. 4.5% rate, compounded daily, $10,000 for a year
APY = 4.602%. You earn $460.25 in interest instead of $450 with simple interest. With monthly compounding, the APY is 4.594% and the interest $459.40.
| Compounding | APY at 4.5% |
|---|---|
| Daily | 4.602% |
| Monthly | 4.594% |
| Quarterly | 4.577% |
| Semiannually | 4.551% |
| Annually | 4.500% |
| Continuous | 4.603% |
2. A 4.50% APY, back to the rate
With daily compounding, the nominal rate behind a 4.50% APY is 4.402%, and $10,000 earns $450 in a year. With monthly compounding, the rate is 4.410%, and $25,000 kept for 18 months earns $1,706.34.
3. A 6-month CD at 3.9%, compounded quarterly
APY = 3.957%. A $5,000 deposit earns $97.98 over 6 months.
Reading the result
APY is the number to compare between accounts because it already includes compounding. The interest projection assumes a fixed rate; on savings and money market accounts the rate is usually variable and can change after you open the account. Taxes on interest aren't included.
Frequently asked questions
What is the difference between APR and APY?
APR is the nominal annual rate before compounding. APY is the yield you actually earn in a year once interest earns interest. A 4.5% rate compounded daily gives a 4.602% APY.
Does daily compounding make a big difference?
Less than you might expect at typical savings rates. On $10,000 at 4.5%, daily compounding earns $460.25 a year and monthly compounding $459.40, a difference of 85 cents. The gap widens at higher rates: 12% compounded monthly is a 12.683% APY.
How do I convert APY to an interest rate?
Use APR = n × ((1 + APY)^(1/n) − 1). A 4.50% APY compounded daily corresponds to a 4.402% rate; compounded monthly, to 4.410%. Choose APY → APR in the calculator to do this automatically.
How much interest will I earn in a few months?
Enter the term in months. The calculator compounds the APY for that fraction of a year: $5,000 at 3.9% compounded quarterly earns $97.98 in 6 months, assuming the rate doesn't change.
Why is continuous compounding only slightly higher than daily?
Compounding more often has diminishing returns. At 4.5%, daily compounding gives 4.602% and continuous compounding, the mathematical limit, 4.603%.
Is my money safe in a high-APY account?
The APY says nothing about safety. Deposits at FDIC-insured banks are covered up to $250,000 per depositor, per insured bank, for each account ownership category. Check that the institution is insured before you deposit.
Sources
This calculator provides estimates for educational purposes and is not financial advice. Your bank's disclosures and account agreement determine the interest you actually earn.