How to use this calculator
- Nominal yearly rate (APR). Enter the stated yearly rate before compounding.
- Compounding frequency. Choose how often interest is added to the balance.
- Deposit amount. Enter the sum you want to test.
The results show the APY, the interest in the first year and the balance after one year. A table then compares the APY for the same nominal rate at yearly, twice-yearly, quarterly, monthly, daily and continuous compounding.
The first-year figures assume the deposit stays untouched for twelve months and the rate does not change.
Worked example
These are the starting values in the calculator above and the results they give. Change any input to see your own numbers.
- Stated yearly rate (APR)
- 5%
- Compounding
- Monthly
- Deposit
- $10,000
- APY
- 5.116%
- Interest in the first year
- $511.62
- Balance after one year
- $10,512
- Extra over simple interest
- $11.62
How APY is calculated
A nominal rate is split across the compounding periods in a year. With monthly compounding, one twelfth of the yearly rate is applied each month. Each time interest is added, the balance grows, and the next period's interest is worked out on the larger balance.
APY measures the total effect of this over one year. The calculator divides the nominal rate by the number of periods, adds 1, raises the result to the power of the number of periods, then subtracts 1.
Continuous compounding is the limit: interest added at every instant. It uses the mathematical constant e, about 2.718, and gives the highest APY possible for a given nominal rate.
First-year interest is the deposit times the APY. The balance after one year is the deposit plus that interest.
APY = (1 + r ÷ n)^n − 1. Continuous compounding: APY = e^r − 1- APY
- annual percentage yield, as a decimal
- r
- nominal yearly rate (APR) as a decimal
- n
- compounding periods per year (1, 2, 4, 12 or 365)
- e
- mathematical constant, about 2.718
How to read the comparison table
The table shows how much compounding frequency matters for your rate. Three patterns stand out.
- With yearly compounding, APY equals the nominal rate. Interest is added once, so there is no interest on interest within the year.
- More frequent compounding raises APY, but by less each step. The move from yearly to monthly adds more than the move from monthly to daily. Daily and continuous are almost identical.
- The effect is bigger at higher rates. At low rates the APY values across the table are very close. At high rates the gaps widen.
APY is the fair way to compare savings products, because it puts different compounding schedules on the same footing. Two accounts with the same nominal rate can pay different amounts, and the one with the higher APY pays more.
For borrowing, the terms are used differently, and a loan's APR may also include fees. The APR vs APY guide explains the difference, and the APR calculator covers the loan side. To project a balance over many years, use the compound interest calculator.
Frequently asked questions
What is APY?
APY stands for annual percentage yield. It is the real rate of return on a deposit over one year, including the effect of compounding. Because interest is added to the balance and then earns interest itself, APY is equal to or higher than the stated nominal rate. It is the standard figure for comparing savings products.
What is the difference between APR and APY?
APR is the yearly rate without the effect of compounding within the year. APY includes it. For savings, APY shows what you really earn, so it is the more useful number. For loans, APR is the usual quoted figure and may also include certain fees. When compounding happens more than once a year, APY is higher than APR.
How do I convert APR to APY?
Divide the APR, written as a decimal, by the number of compounding periods in a year. Add 1. Raise the result to the power of the number of periods. Subtract 1. Multiply by 100 to show it as a percent. The calculator does these steps for you and repeats them for each common compounding frequency.
Does compounding frequency make a big difference?
At typical savings rates, not a large one. Going from yearly to monthly compounding lifts the yield a little. Going from monthly to daily adds very little more. The nominal rate has a much bigger effect on what you earn than the compounding schedule. Compare APY figures directly to see which option actually pays more.
Is a higher APY always better?
For the interest earned, yes: a higher APY pays more on the same deposit over the same time. But yield is only one factor. Check whether the rate is fixed or can change, whether there are fees or minimum balances, and how easily you can get your money out. A slightly lower APY with fewer conditions can suit some needs better.
This calculator gives estimates for education only. It does not know your full situation and is not financial advice. Reviewed and updated November 15, 2026.