APY Calculator
Turn an interest rate into annual percentage yield (APY), and see how much a deposit earns with different compounding.
Results
| Item | Value |
|---|
APY by compounding
| Compounding | APY | Interest on deposit (1 year) |
|---|
Quick Answer
APY = (1 + r ÷ n)^n − 1, where r is the yearly rate and n is the number of times interest is added each year. A 4.5% rate compounded monthly gives an APY of 4.594%. On $10,000, that earns $459.40 in a year.
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Table of Contents
How This APY Calculator Works
Enter the stated interest rate and how often interest is added. The calculator shows the annual percentage yield, which includes the effect of compounding, plus what a deposit would earn. The second table compares every compounding option at the same rate.
Quick explanation: APY is the real yearly return once interest earns interest.
- APR (rate): the stated yearly rate before compounding.
- Compounding: how often interest is added to your balance.
- APY: always equal to or higher than the rate.
How to Use the APY Calculator
- Enter the interest rate the bank quotes.
- Choose how often interest is compounded.
- Optionally, enter a deposit and the number of years.
- Press Calculate.
- Read the APY and earnings, and compare compounding options in the second table.
Core Formulas
- APY: (1 + r ÷ n)^n − 1
- Continuous compounding: e^r − 1
- Balance after t years: deposit × (1 + APY)^t
r is the yearly rate as a decimal and n is the number of compounding periods a year.
Key Terms
- APY: annual percentage yield, the yearly return including compounding.
- APR: annual percentage rate, the yearly rate before compounding.
- Compounding: adding interest to the balance so it earns interest too.
- Compounding frequency: how many times a year interest is added.
Worked Example
A savings account pays 5% compounded daily.
- APY = (1 + 0.05 ÷ 365)^365 − 1
- APY = 5.127%
- $5,000 earns about $256.34 in a year
Real-Life Examples
- Comparing two banks: 4.40% compounded daily gives 4.498% APY, while 4.45% compounded yearly gives 4.450%. The second pays slightly more.
- A high-yield account: 4.5% compounded monthly on $25,000 earns about $1,148.50 in a year.
- A 3-year CD: $10,000 at a 4.5% rate compounded monthly grows to about $11,442.48.
- Leaving money in for longer: $10,000 at 4.5% compounded monthly grows to about $15,670 after 10 years, with no extra deposits.
- Checking an advert: if an account claims 5.00% APY with monthly compounding, the stated rate is about 4.889%.
APY vs APR
- APR: annual percentage rate, the yearly rate without compounding. Used mostly for loans.
- APY: annual percentage yield, the yearly return with compounding. Used for savings.
- Which is higher: APY is higher whenever interest compounds more than once a year.
- For loans: try our APR Calculator.
APY at Common Rates
| Rate | Monthly APY | Daily APY |
|---|---|---|
| 1% | 1.005% | 1.005% |
| 2% | 2.018% | 2.020% |
| 3% | 3.042% | 3.045% |
| 4% | 4.074% | 4.081% |
| 4.5% | 4.594% | 4.602% |
| 5% | 5.116% | 5.127% |
| 6% | 6.168% | 6.183% |
Comparing Savings Offers
- Compare APY, not rate: APY puts different compounding on equal terms.
- Rate changes: savings rates can change. CD rates are usually fixed.
- Fees and minimums: fees or balance rules can lower your real return.
- Insurance: check that the bank or credit union is FDIC or NCUA insured.
Common Mistakes to Avoid
- Comparing a rate with an APY. Turn both into APY first.
- Expecting big gains from daily compounding. It adds only a little over monthly.
- Ignoring fees. A monthly fee can wipe out the interest on small balances.
- Assuming the rate is fixed. Savings rates often change.
- Forgetting tax. Interest is usually taxable.
Frequently Asked Questions
APY = (1 + rate ÷ n)^n − 1, where n is how many times interest compounds each year. This calculator does it for you.
About 5.116%.
Neither is better. APY shows what you earn on savings, and APR shows the yearly cost of borrowing before compounding.
Only a small one. At 5%, daily gives about 5.127% APY and monthly about 5.116%.
US rules require banks to show APY on deposit accounts so people can compare offers fairly.
Yes, on savings accounts with variable rates. A CD usually locks in its APY for the term.
About $450 in one year, before tax, if the rate stays the same.
Use rate = n × ((1 + APY)^(1 ÷ n) − 1). For 5% APY compounded monthly, the rate is about 4.889%.
Not always. Many banks list both. The APY includes compounding, so it is the better number to compare.
No. APY describes how one balance grows in a year. Regular deposits earn interest from the day they arrive.
It depends on current market rates. Compare high-yield savings accounts, money market accounts and CDs at the time you open one.
Often yes. Many banks work out interest daily and add it to the account monthly. The APY already reflects this.
Loans usually quote APR. The effective yearly cost with compounding is similar to APY and is sometimes called the effective annual rate.
References & Sources
| Source | Used For | Link |
|---|---|---|
| Consumer Financial Protection Bureau, Regulation DD (Truth in Savings) | How APY must be shown. | https://www.consumerfinance.gov/rules-policy/regulations/1030/ |
| Wikipedia, Annual percentage yield | The APY formula. | https://en.wikipedia.org/wiki/Annual_percentage_yield |