This calculator gives estimates for education and planning. It is not investment, tax or legal advice; for decisions about your own situation, talk to a qualified financial professional.
Two numbers for the same rate
A rate of “6% compounded monthly” really means 0.5% a month. Over a year, each month’s interest also earns interest, so the balance grows by more than 6%. Banks and lenders therefore quote two numbers:
- APR (annual percentage rate): the nominal rate, the periodic rate times the number of periods in a year.
- APY (annual percentage yield), or effective annual rate (EAR): what you actually earn or pay over a year once compounding is included.
In the United States, the Truth in Savings Act requires banks to quote the APY on deposit accounts, so savers can compare accounts with different compounding. Loans are quoted with the APR, which looks lower.
The formulas
- From APR to APY: APY = (1 + APR ÷ n)ⁿ − 1
- From APY to APR: APR = n × ((1 + APY)^(1/n) − 1)
- Continuous compounding: APY = e^APR − 1, and APR = ln(1 + APY)
where n is the number of compounding periods per year.
Example
A 6% APR compounded monthly:
- Monthly rate: 0.5%
- APY: (1.005)¹² − 1 = 6.168%
- Continuous equivalent rate: 5.985%
- Interest over one year on $10,000: $616.78
How compounding frequency changes the APY
At a 6% APR:
| Compounding | APY |
|---|---|
| Annually | 6.000% |
| Quarterly | 6.136% |
| Monthly | 6.168% |
| Daily | 6.183% |
| Continuously | 6.184% |
Most of the gain comes from moving away from annual compounding. Beyond monthly, the difference is tiny.
Practical uses
- Comparing savings accounts: always compare APYs, not rates with different compounding.
- Credit cards: card APRs are applied daily or monthly, so a 24% APR costs about 26.8% a year if the balance is carried and interest compounds monthly.
- Investments: annual returns reported by funds are already effective rates.
- Converting between periods: the equivalent monthly rate, (1 + APY)^(1/12) − 1, is the one to use in a spreadsheet when you start from an annual effective rate.
Fees are separate
The APR disclosed on a US loan under the Truth in Lending Act can include fees such as origination charges or mortgage points. This calculator only converts between interest rates; to include fees, use the loan cost calculator.