Interest Rate Calculator

APR vs APY

APR
Annual Percentage Rate - the base rate without compounding
APY
Annual Percentage Yield - the effective rate with compounding
Formula
APY = (1 + APR/n)^n - 1

Understanding Interest Rates

APR vs APY: What's the Difference?

Understanding the difference between APR and APY is crucial for comparing financial products. Banks often advertise APY for savings accounts (higher number looks better) and APR for loans (lower number looks better).

APR (Annual Percentage Rate)

  • The simple annual interest rate
  • Does not account for compounding
  • Used for loans and credit cards
  • Required by law for loan disclosures
  • Makes loan costs appear lower

APY (Annual Percentage Yield)

  • The effective annual rate
  • Includes the effect of compounding
  • Used for savings and investments
  • Shows actual annual return
  • Always higher than APR (if compounded)

APR to APY Conversion

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

Where n = number of compounding periods per year

APRAPY (Monthly)APY (Daily)Difference
3%3.042%3.045%+0.045%
5%5.116%5.127%+0.127%
10%10.471%10.516%+0.516%
20%21.939%22.134%+2.134%

Finding the Required Interest Rate

Sometimes you need to find what interest rate is required to reach a financial goal. The formula to find the rate is:

r = n × ((FV/PV)^(1/(n×t)) - 1)

Where: FV = Future Value, PV = Present Value, n = compounds/year, t = years

Practical Examples

Example 1: Finding Required Rate

You have $10,000 and want $20,000 in 10 years. What rate do you need?

r = 12 × (($20,000/$10,000)^(1/(12×10)) - 1) = 6.93% APR (7.17% APY)

Example 2: Comparing Savings Accounts

Bank A offers 4.5% APR compounded monthly. Bank B offers 4.45% APR compounded daily. Which is better?

Bank A APY: 4.594% | Bank B APY: 4.548% = Bank A wins by 0.046%

Why This Matters

For Savers

Always compare APY, not APR, when choosing savings accounts. A higher compounding frequency can make a lower APR account actually better.

For Borrowers

Credit card companies quote APR, but you actually pay APY. A 20% APR credit card costs 21.9% annually when compounded monthly - almost 2% more!

Key Takeaway

The higher the interest rate and the more frequent the compounding, the bigger the difference between APR and APY. This difference can significantly impact your savings growth or loan costs over time. Always calculate or compare APY for an apples-to-apples comparison.

Frequently Asked Questions

What is the difference between APR and APY?

APR (Annual Percentage Rate) is the simple annual interest rate without compounding. APY (Annual Percentage Yield) is the effective rate including compound interest. APY is always higher than APR when interest compounds. For example, 5% APR compounded monthly equals 5.12% APY. Always compare APY for accurate comparisons.

How do I convert APR to APY?

Use the formula: APY = (1 + APR/n)^n - 1, where n is the number of compounding periods per year. For 5% APR compounded monthly: APY = (1 + 0.05/12)^12 - 1 = 5.116%. The more frequently interest compounds, the higher the APY relative to APR.

Why do banks advertise APY for savings but APR for loans?

Banks want to make their products look attractive. APY is higher than APR, so advertising APY makes savings accounts look better. APR is lower than APY, so advertising APR makes loans look cheaper. By law, APR must be disclosed for loans, but the APY is what you actually pay. Always calculate the true cost.

How do I find what interest rate I need to reach a goal?

Use the rate formula: r = n x ((FV/PV)^(1/(n x t)) - 1), where FV is future value, PV is present value, n is compounds per year, and t is years. For example, to double $10,000 to $20,000 in 10 years with monthly compounding, you'd need about 6.9% APR (7.17% APY).