5% APR compounded monthly
- Input
- APR = 5%, Compounding = monthly (m = 12)
- Working
- APY = (1 + 0.05/12)^12 − 1 = (1.004167)^12 − 1 = 1.051162 − 1 = 0.051162, which is 5.1162%, shown rounded as 5.12%.
- Result
- 5% APR, monthly compounding → APY = 5.12%
APY Calculator
Convert a stated APR into the true annual percentage yield for any compounding frequency — monthly, daily or continuous — so savings offers can be compared fairly. Runs entirely in your browser — your numbers never leave this device.
Compounding
APY (effective annual yield)
5.12%
Exactly 5.1162% when monthly compounding is applied to a 5.00% APR.
| Compounding | Times per year | APY |
|---|---|---|
| Annually | 1 | 5.0000% |
| Semi-annually | 2 | 5.0625% |
| Quarterly | 4 | 5.0945% |
| Monthly | 12 | 5.1162% |
| Daily | 365 | 5.1267% |
| Continuously | ∞ | 5.1271% |
APY is always at least the APR, and the gap grows the more often interest compounds — daily and continuous compounding differ by only a whisker.
How it works
APY = (1 + APR/m)^m − 1, where m = compounding periods per year | Continuous compounding: APY = e^(APR) − 1, with APR as a decimal in both formulas
| Compounding | Periods per year (m) | APY |
|---|---|---|
| Annual | 1 | 5.00% |
| Semi-annual | 2 | 5.06% |
| Quarterly | 4 | 5.09% |
| Monthly | 12 | 5.12% |
| Daily | 365 | 5.13% |
| Continuous | Limit | 5.13% |
APR and APY describe the same account in different ways. APR (annual percentage rate) is the stated yearly rate before compounding within the year; APY (annual percentage yield) is what $100 actually becomes after a year once the compounding is included. Because interest credited mid-year itself earns interest for the rest of the year, APY is always equal to or higher than APR — equal only when interest is credited exactly once a year. This calculator converts between them for any compounding frequency.
Frequency is the whole difference. Monthly crediting gives interest twelve chances a year to start earning its own interest; daily crediting gives 365; continuous compounding is the mathematical limit, where interest is credited constantly. The gaps shrink as frequency rises — monthly already captures most of the possible gain over annual, and daily adds only a fraction more — and the examples show the full ladder on the same 5% APR so the size of each step is concrete.
APY is the right number for comparing savings accounts, because it puts every offer on the same effective footing regardless of how often each one credits interest. Two accounts at the same APR but different frequencies do not pay the same; two accounts at the same APY do (before fees, minimum-balance rules and rate changes, which APY does not capture and which are worth checking in the account terms).
Worked examples
What the APY difference is worth on $1,000 for one year
- Input
- Deposit = $1,000, APR = 5%, One year, Annual vs monthly compounding
- Working
- Annual: 1,000 × 1.05 = $1,050.00, interest $50.00. Monthly: 1,000 × (1 + 0.05/12)^12 = 1,000 × (1.004167)^12 ≈ $1,051.16, interest ≈ $51.16. The APY gap of 0.12 percentage points is worth $1.16 on $1,000 in one year — and scales with the balance and with every further year the money stays.
- Result
- Monthly compounding earns ≈ $51.16 versus $50.00 — $1.16 more per $1,000 in year one
6% APR compounded monthly
- Input
- APR = 6%, Compounding = monthly (m = 12)
- Working
- APY = (1 + 0.06/12)^12 − 1 = (1.005)^12 − 1 = 1.061678 − 1 = 0.061678, which is 6.1678%, rounded to 6.17%. The compounding uplift (0.17 points) is larger than at 5% APR (0.12 points) because there is more interest in the year to compound.
- Result
- 6% APR, monthly compounding → APY = 6.17%
Frequently asked questions
Which is bigger, APR or APY?
APY is bigger whenever interest compounds more than once a year, and equal to APR when it compounds annually. APR is the nominal stated rate; APY adds the effect of interest earning interest within the year. A 5% APR compounded monthly is a 5.12% APY — the account pays as if the rate were 5.12% credited once a year.
Why do banks quote APY for savings and APR for loans?
Each quote shows the number that regulation and convention attach to the product, and each flatters its side: APY makes a savings yield look as large as it truly is after compounding, while loan APR folds the interest rate and certain fees into one borrowing cost. For comparing two savings accounts, compare APY with APY; for comparing loans, compare APR with APR — mixing the two measures misleads.
How much difference does daily versus monthly compounding make?
Very little. At 5% APR, monthly compounding gives a 5.12% APY and daily gives 5.13% — a hundredth of a percentage point, worth about 10 cents a year per $1,000. The jump from annual (5.00%) to monthly (5.12%) is where almost all of the frequency effect lives; beyond monthly, the returns to more frequent crediting are tiny.
What is continuous compounding?
The limiting case where interest is credited at every instant rather than in discrete periods. Its formula uses the constant e: APY = e^(APR) − 1. At 5% APR that gives ≈ 5.1271%, or 5.13% rounded — barely above daily compounding, which is why continuous compounding matters mainly in financial mathematics rather than in comparing real accounts.
Does APY account for fees or rate changes?
No. APY is calculated from the rate and compounding frequency alone, assuming the rate holds for a full year. Account fees, minimum-balance requirements and variable rates that change mid-year all alter what you actually earn. APY is the correct starting comparison, not the whole comparison.
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