How do you calculate APY from an interest rate?
Divide the rate by the number of compounding periods, add 1, raise that to the number of periods, then subtract 1. Here, r is the yearly rate and n is the number of periods a year.
APY = (1 + r ÷ n)^n − 1With 4% compounded monthly, r ÷ n is 0.33333% a month. Compounded over 12 months, it's an APY of 4.074%. For continuous compounding, the limit of that formula uses the constant e, which is about 2.71828:
APY = e^r − 1| Compounding | Rate per period | APY | Interest in a year |
|---|---|---|---|
| Yearly | 4.00000% | 4.000% | $400.00 |
| Quarterly | 1.00000% | 4.060% | $406.04 |
| Monthly | 0.33333% | 4.074% | $407.42 |
| Weekly | 0.07692% | 4.079% | $407.95 |
| Daily | 0.01096% | 4.081% | $408.08 |
| Continuous | None | 4.081% | $408.11 |
In this tool, "APR" means the stated yearly rate before compounding. Banks often call that the interest rate on a savings account or CD. Regulation DD defines the interest rate as the annual rate of interest that doesn't reflect compounding, and APY as the percentage rate reflecting the total interest paid, based on that rate and the compounding frequency for a 365-day period.
How do you convert APY back to APR?
Run the formula backward. An APY of 5% with monthly compounding comes from a stated rate of 4.889%. The stated rate you get depends on the schedule, while the APY stays fixed.
r = n × [(1 + APY)^(1 ÷ n) − 1]| APY | Yearly | Quarterly | Monthly | Weekly | Daily | Continuous |
|---|---|---|---|---|---|---|
| 2% | 2.000% | 1.985% | 1.982% | 1.981% | 1.980% | 1.980% |
| 3% | 3.000% | 2.967% | 2.960% | 2.957% | 2.956% | 2.956% |
| 4% | 4.000% | 3.941% | 3.928% | 3.924% | 3.922% | 3.922% |
| 5% | 5.000% | 4.909% | 4.889% | 4.881% | 4.879% | 4.879% |
| 6% | 6.000% | 5.870% | 5.841% | 5.830% | 5.827% | 5.827% |
| 8% | 8.000% | 7.771% | 7.721% | 7.702% | 7.697% | 7.696% |
| 10% | 10.000% | 9.645% | 9.569% | 9.540% | 9.532% | 9.531% |
You rarely need this for shopping, since APY is the number to compare. It helps when you want the monthly interest on a balance, since interest for one period is the balance times the stated rate divided by the periods in a year.
How much more does daily compounding earn than monthly?
Yes, but by very little. At 4%, daily compounding beats monthly by 0.007% of APY, or $0.67 a year on $10,000. A rate just 0.25 points higher adds 0.260%. So the rate matters far more than the schedule, until rates get high.
| Stated rate | Yearly | Quarterly | Monthly | Weekly | Daily | Continuous |
|---|---|---|---|---|---|---|
| 1% | 1.000% | 1.004% | 1.005% | 1.005% | 1.005% | 1.005% |
| 2% | 2.000% | 2.015% | 2.018% | 2.020% | 2.020% | 2.020% |
| 3% | 3.000% | 3.034% | 3.042% | 3.045% | 3.045% | 3.045% |
| 4% | 4.000% | 4.060% | 4.074% | 4.079% | 4.081% | 4.081% |
| 5% | 5.000% | 5.095% | 5.116% | 5.125% | 5.127% | 5.127% |
| 10% | 10.000% | 10.381% | 10.471% | 10.506% | 10.516% | 10.517% |
| 25% | 25.000% | 27.443% | 28.073% | 28.326% | 28.392% | 28.403% |
Notice that going from daily to continuous hardly changes anything at savings rates. Continuous compounding is the upper limit, not a large extra gain. On a 24.99% rate the gap is wider, which is why compounding matters more on debt than on savings.
How much will an APY pay per month?
Divide the year's interest by 12 for a rough average. At 4.07% APY, $10,000 earns $407.42 in a year, or about $33.95 a month on average. The exact first month is $33.33, and each later month is slightly more, since interest builds on interest.
| Balance | 3% a year | 3% a month | 4% a year | 4% a month | 5% a year | 5% a month |
|---|---|---|---|---|---|---|
| $1,000 | $30.00 | $2.50 | $40.00 | $3.33 | $50.00 | $4.17 |
| $5,000 | $150.00 | $12.50 | $200.00 | $16.67 | $250.00 | $20.83 |
| $10,000 | $300.00 | $25.00 | $400.00 | $33.33 | $500.00 | $41.67 |
| $25,000 | $750.00 | $62.50 | $1,000.00 | $83.33 | $1,250.00 | $104.17 |
| $50,000 | $1,500.00 | $125.00 | $2,000.00 | $166.67 | $2,500.00 | $208.33 |
| $100,000 | $3,000.00 | $250.00 | $4,000.00 | $333.33 | $5,000.00 | $416.67 |
APY by itself says nothing about deposits. Regulation DD assumes the principal and interest stay on deposit, with no other transactions, for the entire term. If you add money each month, your interest depends on when it arrives. Add a monthly amount under advanced options, or use our savings calculator to work toward a goal.
Why APR on a loan isn’t the opposite of APY on savings
The two labels come from different rules. APY on a deposit reflects only interest, and Regulation DD says it doesn't include the value of a bonus for opening an account. APR on a loan can reflect fees as well. The Consumer Financial Protection Bureau (CFPB) says a mortgage APR reflects the interest rate, any points, mortgage broker fees, and other charges. So a mortgage APR isn't a stated rate you can plug into the formula above.
On a credit card, the math does apply if interest is added to an unpaid balance. A 24.99% APR compounded daily has an effective annual rate of 28.38%. On $5,000 left unpaid for a year, that's $1,418.94 of interest, compared with $1,249.50 with no compounding. In practice you'd have to make payments, so real interest would differ. Check your card agreement for how interest compounds.
This tool can't turn a loan APR into a lender's true cost. To work out an APR from a loan's fees and payments, use our APR calculator. A car loan with fixed monthly payments doesn't build interest on interest when you pay on time.
When an advertised APY doesn’t tell the whole story
Under Regulation DD, banks calculate APY with a general formula that works from real interest and days. For example, $61.68 of interest on $1,000 over 365 days is 6.17% APY.
APY = 100 × [(1 + interest ÷ principal)^(365 ÷ days in term) − 1]- Variable rates. A savings account's rate can change after you open it, so the APY today isn't a promise for the year.
- Tiers and teaser rates. An account may pay different rates at different balances or during an opening period. The label may not reflect your balance.
- Fees. APY reflects interest, so a monthly account fee can eat into what you actually keep. A $5 monthly fee is $60 a year, which takes 3% off a $2,000 balance.
- Yields outside banks. Regulation DD applies to depository institutions, except credit unions, so a yield quoted by a crypto or investment platform isn't a Regulation DD APY. Treat it with care, since returns and risks can be very different.
- Tax and inflation. APY is before both. Our CD calculator shows the effect on a term deposit.
For a real account, the bank's account disclosure is the document to rely on. For the bigger idea behind all of this, read how compound growth really works.
Common questions
What is the difference between APY and interest rate?
The interest rate is the yearly rate before compounding. APY includes compounding, so it's equal or higher. A 4% rate compounded daily is 4.08% APY. If interest compounds once a year, they match.
Does APY already include compounding?
Yes. If an account pays 4% APY, $10,000 left alone for a year earns $400, whatever the schedule. Don't apply the compounding formula to an APY a second time.
Can I use this for a CD or a money market account?
Yes, if you have a stated rate and a schedule. The same math applies to any account that compounds interest. For a CD's maturity value and early withdrawal cost, use our CD calculator.
What is a periodic rate?
It's the rate for a single compounding period. Select "Rate per period," then enter it with the schedule. A rate of 0.05% a day is 18.25% APR and an APY of 20.02%.
What is a good APY?
This tool doesn't track rates, and they change often. Compare APYs from several insured banks for the same type of account on the same day, and check for fees and balance rules.
Sources
- Regulation DD, Appendix A: Annual Percentage Yield Calculation · Consumer Financial Protection Bureau
- Regulation DD, § 1030.2: Definitions · Consumer Financial Protection Bureau
- Regulation DD, § 1030.1: Authority, purpose, coverage · Consumer Financial Protection Bureau
- What is the difference between a mortgage interest rate and an APR? · Consumer Financial Protection Bureau