Effective Interest Rate Calculator

What is Effective Interest Rate?

The effective interest rate (also called effective annual rate or annual equivalent rate) is the actual interest rate earned or paid on an investment or loan after accounting for compounding within a given time period. It differs from the nominal rate because it considers the effect of compounding.

When comparing financial products with different compounding frequencies, the effective interest rate provides a true 'apples-to-apples' comparison. A 6% nominal rate compounded monthly is actually higher than 6% compounded annually due to the compounding effect.

Effective Interest Rate Formulas

The formulas for calculating effective interest rates are:

Effective Period Rate = Nominal Annual Rate ÷ n

Effective Annual Rate = (1 + Nominal Rate ÷ n)^n - 1

Where:

• Nominal Rate = Stated annual interest rate (in decimal form)
• n = Number of compounding periods per year
• EAR = Effective Annual Rate (also called APY)

Example Calculations

Example 1: Monthly Compounding

Calculate the effective annual rate for a nominal rate of 6% compounded monthly:

EAR = (1 + 0.06/12)^12 - 1 = (1.005)^12 - 1 = 0.061678 = 6.17%

The effective annual rate is 6.17%, which is 0.17% higher than the nominal rate

Example 2: Daily Compounding

Calculate the effective annual rate for a nominal rate of 5% compounded daily:

EAR = (1 + 0.05/365)^365 - 1 = 0.051267 = 5.13%

The effective annual rate is 5.13%, which is 0.13% higher than the nominal rate

Compounding Frequency Comparison

For a nominal rate of 6%, here's how the effective rate changes with compounding frequency:

• Annually (n=1): 6.00%
• Semi-Annually (n=2): 6.09%
• Quarterly (n=4): 6.14%
• Monthly (n=12): 6.17%
• Weekly (n=52): 6.18%
• Daily (n=365): 6.18%
• Continuous: 6.18% (limit as n approaches infinity)

Common Applications

• Comparing savings accounts with different compounding frequencies
• Evaluating investment returns accurately
• Comparing credit card APR with different billing cycles
• Analyzing loan offers from different lenders
• Certificate of deposit (CD) rate comparisons
• Bond yield calculations
• Mortgage rate comparisons
• Understanding true cost of borrowing

Why Effective Interest Rate Matters

• More accurate comparison: Compare products with different compounding
• True return calculation: Shows actual earnings or costs
• Regulatory compliance: Many countries require EAR disclosure
• Better decision making: Choose the best financial products
• Compounding awareness: Understand the power of compounding
• Hidden costs: Reveals true cost of loans and credit

Tips for Using Effective Interest Rate Calculator

• Always compare effective rates, not nominal rates
• More frequent compounding results in higher effective rates
• For investments, look for higher effective rates
• For loans, look for lower effective rates
• Check if the rate is APR (nominal) or APY (effective)
• Consider fees and other costs not included in the rate
• Use effective rate for long-term financial planning

APR vs APY

APR: APR (Annual Percentage Rate): Nominal rate, doesn't account for compounding. Used for loans and credit cards.

APY: APY (Annual Percentage Yield): Effective rate, accounts for compounding. Used for savings and investments.

If a savings account offers 5% APR compounded monthly, the APY is 5.12%. You'll actually earn 5.12%, not 5%.