How to use it
- APR ↔ APY: enter a rate, say whether it's the nominal rate or the effective rate, and pick how often interest is compounded. The table shows the same nominal rate at every frequency.
- Rate of a loan: enter the amount borrowed, the regular payment and the term. The result is the yearly rate lenders quote (rate per payment × payments a year) and its effective annual rate.
Formulas
Effective rate = (1 + r ÷ n)n − 1, or er − 1 compounded continuously
Nominal rate = n × ((1 + effective)1/n − 1)
Loan: P = M × (1 − (1 + i)−N) ÷ i, solved for the rate i per payment
Here r is the nominal yearly rate, n the number of compounding periods a year, P the loan, M the payment and N the number of payments. The loan rate is found with Newton's method, kept inside a range that always contains the answer and falling back to halving that range, so it never fails to converge.
Worked examples
- 5% compounded daily: (1 + 0.05 ÷ 365)365 − 1 = 5.1267%; continuously, e0.05 − 1 = 5.1271%. Compounding more often adds less and less.
- Car loan: $20,000 repaid at $396.02 a month for 60 months. The rate that makes 60 payments worth exactly $20,000 today is 0.5833% a month, so 7% a year (7.23% effective). You pay $3,761.20 of interest.
- The CFPB's sample Loan Estimate shows $162,000 at 3.875% for 30 years with a $761.78 monthly payment. Entering that payment gives back 3.875%.
Tips
- Compare savings accounts on APY (AER) and loans on APR including fees: those are the like-for-like figures.
- For a full repayment schedule use the EMI calculator or the mortgage calculator; to see growth over time, the compound interest calculator.
- Canadian fixed-rate mortgages are compounded twice a year (the Interest Act requires the rate to be stated that way), which the mortgage calculator handles for you.
APY definition from the US Truth in Savings rules (Regulation DD, Appendix A), checked 2 October 2026. An estimate, not financial advice.