Equivalent Rate Calculator

What is an Equivalent Rate?

An Equivalent Rate allows you to compare interest rates with different compounding frequencies on an equal basis. It answers questions like: "What monthly compounding rate equals 5% annual rate compounded quarterly?"

Key Terms

APR (Annual Percentage Rate)

The nominal or stated annual interest rate without accounting for compounding. This is the rate often advertised by banks and lenders.

APY (Annual Percentage Yield)

Also called the Effective Annual Rate (EAR), this is the actual rate of return or cost after accounting for compound interest. APY reflects what you actually earn (or pay).

The Formulas

APR to APY (Effective Annual Rate)

APY = (1 + APR/n)^n - 1

Where:

• APR = Annual Percentage Rate (as decimal)
• n = Number of compounding periods per year

APY to APR (Nominal Rate)

APR = n × ((1 + APY)^(1/n) - 1)

Where:

• APY = Annual Percentage Yield (as decimal)
• n = Number of compounding periods per year

Converting Between Compounding Frequencies

Equivalent Rate = n₂ × ((1 + r₁/n₁)^(n₁/n₂) - 1)

Where:

• r₁ = Original nominal rate
• n₁ = Original compounding periods
• n₂ = Target compounding periods

Compounding Frequencies

Continuous Compounding

For continuous compounding, use::

• APR to APY: APY = e^APR - 1
• APY to APR: APR = ln(1 + APY)

Where e ≈ 2.71828 (Euler's number)

How to Use This Calculator

1. Select calculation mode:

   • APR to APY: Convert nominal rate to effective rate
   • APY to APR: Convert effective rate to nominal rate
   • Equivalent Rate: Convert rate from one compounding to another

2. Enter your rate as a percentage

3. Choose compounding frequency for the rate

4. View results showing the converted rate and comparison

Practical Examples

Example 1: Savings Account

A bank offers 5% APR compounded monthly.

• APY = (1 + 0.05/12)^12 - 1 = 5.12%

Example 2: Credit Card

A credit card has 24% APR compounded daily.

• APY = (1 + 0.24/365)^365 - 1 = 27.11%

Example 3: Investment Comparison

Comparing 4.8% quarterly vs 4.75% monthly:

• 4.8% quarterly APY = 4.89%
• 4.75% monthly APY = 4.85%
• The quarterly option is actually better!

Why It Matters

• For Savers: Higher compounding frequency means more interest earned
• For Borrowers: More frequent compounding means you pay more in interest
• For Investors: APY gives the true rate of return for comparison

Frequently Asked Questions

Is a higher APR or APY better?

For savings, you want higher rates. For loans, lower is better. APY gives the true picture for comparison.

Why is APY always higher than APR?

Because APY includes the effect of compound interest. Only with annual compounding are APR and APY equal.

Which compounding is best for savings?

More frequent compounding (daily or continuous) yields higher returns, assuming the same APR.

Note: This calculator provides estimates for educational purposes. Actual rates may vary based on specific financial institution policies.