APY calculator
This APY calculator turns the nominal rate (APR) into the effective annual yield (APY). Example: 5% APR compounded monthly gives 5.1162% APY; on 10,000 that is 511.62 of interest a year.
Example: Conversion: APR → APY · Nominal rate APR (%) 5 · Compounding periods per year: monthly (12) · Deposit (optional) 10,000 → Result: APY = 5.1162%. Source: Wikipedia – Annual percentage yield. Updated: .
How it is calculated
The APY (annual percentage yield) is the effective annual rate: the return over one year including compound interest. The APR (annual percentage rate) is the nominal rate without that effect. The more often interest is credited, the wider the gap.
Formulas
APY = (1 + APR ÷ n)^n − 1 for n compounding periods a year; with continuous compounding APY = e^APR − 1. In reverse, APR = n × ((1 + APY)^(1/n) − 1) or ln(1 + APY). The calculator’s table shows all compounding types side by side.
Example
5% APR compounded monthly: (1 + 0.05 ÷ 12)^12 − 1 = 5.1162%. On 10,000 that earns 511.62 a year, not 500. Daily compounding gives 5.1267%, continuous 5.1271%; going back from 5.1162% monthly returns 5% APR.
- With annual compounding APR and APY are the same.
- Fees, taxes and changing rates are not included.
Frequently asked questions
What is the difference between APR and APY?
APR is the nominal rate, APY the effective rate including compounding. 5% APR compounded monthly equals 5.1162% APY.
How do you convert APR to APY?
With APY = (1 + APR ÷ n)^n − 1. For 5% and n = 12 that gives 5.1162%.
Why is APY higher than APR?
Because interest already credited earns interest itself in later periods. The more often it is credited, the stronger this compounding effect.
Sources and legal basis
- Wikipedia – Annual percentage yield
- Wikipedia – Compound interest (Periodic compounding, continuous compounding)
- Brealey, Myers, Allen: Principles of Corporate Finance – Effective annual interest rate
As of: · Editorial policy
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