Convert nominal interest rates to effective annual yield (EAY/APY). Compare compounding frequencies and see the difference in future value.
When comparing savings accounts, CDs, or loans, the nominal (stated) interest rate can be misleading. A 5% rate compounded monthly actually yields more than a 5% rate compounded annually. The Effective Annual Yield (EAY), also known as APY, accounts for this compounding effect and gives you the true annual return.
The difference between nominal and effective rates may seem small for low rates and common compounding, but it becomes significant for higher rates, more frequent compounding, and longer time horizons. A credit card charging 24% APR compounded daily has an effective rate of 27.11% — a meaningful difference.
This calculator converts any nominal rate to its effective annual yield based on compounding frequency, and lets you compare two different rate/frequency combinations side by side. The frequency impact table shows how the same nominal rate produces different effective yields across compounding intervals, from annual to continuous. Check the example with realistic values before reporting.
Banks advertise nominal rates that look different from the actual yield. This calculator reveals the true cost or return so you can make accurate comparisons between financial products that compound at different frequencies. Keep these notes focused on your operational context. Tie the context to the calculator’s intended domain. Use this clarification to avoid ambiguous interpretation.
EAY = (1 + r/n)^n − 1 Continuous EAY = e^r − 1 Future Value = Principal × (1 + EAY)^Years Where r = nominal annual rate, n = compounding periods per year.
Result: EAY = 5.1162%
A 5% nominal rate compounded monthly yields an effective annual rate of 5.1162%. On $10,000 over 5 years, this compounds to $12,834 vs $12,763 with annual compounding — a $71 benefit from monthly compounding.
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APR is the nominal annual rate without compounding. APY (= EAY) includes the effect of compounding. APY is always equal to or higher than APR.
Yes, but the difference decreases as frequency increases. Monthly to daily is a bigger jump than daily to continuous for most real-world rates.
It is the mathematical limit of compounding infinitely often. The formula uses e^r. It produces the maximum possible effective rate for a given nominal rate.
Always compare effective rates (APY) between products. A 4.9% APY is better than a 5.0% APR compounded annually (which is exactly 5.0% APY), but worse than 5.0% compounded monthly (5.12% APY).
For borrowers, more frequent compounding means you pay more interest. Credit cards compounding daily cost more than the stated APR suggests.
For fixed-rate products (CDs, fixed savings), yes. For variable-rate products, the APY changes when the underlying rate changes.