Interest Rate Calculator - Convert Nominal to Effective APY & APR

Formula

i = (1 + i⁽ᵐ⁾/m)ᵐ - 1

Enter Values

Nominal Annual Rate (%) *

The nominal or advertised rate (i⁽ᵐ⁾ in actuarial notation). Banks often quote this rate. Always state the compounding frequency with nominal rates.

Compounding Frequency *

Compounding frequency: how many times per year interest is applied. US mortgages typically use m=12 (monthly), Canadian mortgages use m=2 (semi-annual), savings accounts often use m=365 (daily).

Results

Interpretation

For 6% nominal rate compounded monthly: Effective Annual Rate (APY) = 6.1678% | Periodic Rate (monthly) = 0.5000%. This means $10,000 grows to $10,616.78 in one year. Use to compare with competitor offering 6.15% compounded annually (which is lower).

How It Works

The effective rate (i) represents the true annual return, while the nominal rate i⁽ᵐ⁾ is the stated rate compounded m times per year. When m=1, effective = nominal. When m>1, effective > nominal. Also called APY (Annual Percentage Yield).

Key Points

Essential for comparing savings accounts, CDs, and credit cards.
APY = effective rate; APR ≈ nominal rate (before fees).
Use to find true yield before making investment decisions.
Required for regulatory disclosure calculations (Truth in Savings Act).

Continue in this Category

Compound Interest Any Frequency Simple Interest

References

Broverman, S.A. (2015). Mathematics of Investment and Credit (6th Edition). ACTEX Publications. Chapter 1, Section 1.1.2 (pages 8-10) and Section 1.4 (pages 25-31). Equation 1.4 (page 30): (1+i) = (1+i⁽ᵐ⁾/m)ᵐ. Example 1.8 (page 26). Truth in Savings Act (US) requires APY disclosure.

Effective Interest Rate Calculator