Convert a nominal interest rate (APR) and compounding schedule into APY (annual percentage yield). Enter the rate, how often interest compounds, and an optional starting balance to see the effective annual yield and your future balance after a chosen number of years.
Use this to compare savings accounts, CDs, money market funds and any product where compounding frequency matters.
Enter a nominal rate and compounding frequency to see the APY and how a sample starting balance grows over your chosen time horizon.
APY (annual percentage yield) tells you how much your money actually grows in one year once you include compounding. Two accounts can have the same advertised APR but different APYs if they compound interest at different frequencies.
This calculator helps you move from the nominal rate (APR) to the effective rate (APY) and also shows how a sample deposit grows over several years at that yield.
If a bank quotes a nominal annual rate r and compounds interest
m times per year, the APY formula is:
APY = (1 + r/m)^m − 1 r = nominal annual rate (decimal, e.g. 0.045 for 4.5%) m = number of compounding periods per year
For example, 4.5% APR compounded daily (m = 365) has a higher APY than the same rate compounded monthly (m = 12) because interest earned earlier in the year also earns interest.
Daily compounding:
APY = (1 + r/365)^365 − 1
Continuous compounding:
APY = e^r − 1
Continuous compounding assumes interest is added at every instant; it’s mostly used in theoretical finance, but it provides an upper bound on the effect of very frequent compounding.
Once you know the APY, treating it as a one-year growth factor is easy. If
APY is the effective yearly rate and t is the number
of years, then:
Future value = PV × (1 + APY)^t PV = starting balance t = time in years
The calculator uses this to project your balance over your chosen horizon assuming the APY stays constant.
Suppose a savings account advertises 4.5% APR compounded monthly. What is the APY?
APY = (1 + 0.045/12)^12 − 1
≈ (1 + 0.00375)^12 − 1
≈ 1.0460 − 1
≈ 0.0460 = 4.60%
So even though the bank quotes 4.5%, leaving your money in for a year actually grows it by about 4.6%. The calculator performs this conversion instantly.
| Term | Typical use | Includes compounding? |
|---|---|---|
| APR (annual percentage rate) | Loans, mortgages, some savings ads | No — base yearly rate before compounding |
| APY (annual percentage yield) | Savings accounts, CDs, interest-bearing deposits | Yes — effective one-year growth |
| Interest rate | General term; can mean APR or APY | Depends — you must check the context |
| Compounding | Symbol m | Typical usage |
|---|---|---|
| Annually | 1 | Simple bonds, some long-term deposits |
| Semi-annually | 2 | Many fixed income products |
| Quarterly | 4 | Some business and savings products |
| Monthly | 12 | Common for savings accounts and loans |
| Weekly | 52 | Some fintech savings apps |
| Daily | 365 | High-yield savings, money market funds |
If interest is compounded more than once per year, each compounding period earns interest on interest from earlier periods. That extra growth means the effective annual yield (APY) is higher than the nominal rate (APR).
For ordinary compounding (annually, monthly, daily, etc.) and a fixed positive rate, APY is never lower than APR. The only time they match is when interest is compounded exactly once per year.
No. APY is calculated purely from the interest rate and compounding. Account fees reduce your real return, and taxes depend on your personal situation and local rules.
Convert both offers to APY using their APR and compounding details, then compare the APY numbers directly. The higher APY (all else equal) gives you more effective interest per year.