APR to APY Calculator

What is the difference between APR and APY?

When evaluating savings accounts, certificates of deposit (CDs), credit cards, and installment loans, you will encounter two primary annualized interest metrics: Annual Percentage Rate (APR) and Annual Percentage Yield (APY). While both percentages describe interest over a one-year period, they measure fundamentally different financial mechanics.

APR represents the nominal annualized interest rate without taking intra-year compound interest into account. In contrast, APY measures the total effective interest earned or paid across a full year, reflecting how frequently interest is compounded (daily, monthly, or quarterly) and added back to the principal. To calculate deposit returns and multi-year growth projections, use our APY calculator, or evaluate loan APRs with upfront origination fees and closing points using our dedicated APR calculator. When comparing fractional rate spreads or central bank adjustments in basis points, convert units with our basis point calculator.

The mathematical formulas: Converting APR to APY

When interest compounds discretely $m$ times per year at a stated nominal annual rate $\text{APR}$, each compounding cycle earns interest on the accumulated balance. The mathematical formula for discrete compounding is:

Where:

• $\text{APR}$ is the annual percentage rate expressed as a decimal (for example, 0.05 for 5.00%).
• $m$ is the number of compounding periods per year (365 for daily, 12 for monthly, 4 for quarterly, 1 for annual).

For continuous compounding (where interest accrues instantaneously), the equation simplifies using the natural base constant $e \approx 2.71828$:

Reverse conversion: Converting APY to APR

If a bank advertises an APY on a high-yield savings account or CD and you need the underlying periodic interest rate, use our dedicated APY to APR calculator or invert the formula directly:

For continuous compounding, the APY to APR formula uses the natural logarithm:

Published worked example

Suppose a high-yield savings account advertises a nominal APR of 5.00% ($0.05$). Let us examine how the compounding frequency shifts the effective APY:

• Annual Compounding ($m = 1$):
  $\text{APY} = (1 + 0.05/1)^1 - 1 = 5.000\%$
• Monthly Compounding ($m = 12$):
  $\text{APY} = (1 + 0.05/12)^{12} - 1 = (1.004167)^{12} - 1 = 5.116\%$
• Daily Compounding ($m = 365$):
  $\text{APY} = (1 + 0.05/365)^{365} - 1 = (1.00013699)^{365} - 1 = 5.127\%$
• Continuous Compounding ($m = \infty$):
  $\text{APY} = e^{0.05} - 1 = 1.051271 - 1 = 5.127\%$

On an initial deposit of $10,000 held for one year, monthly compounding generates $511.62 in total interest, whereas daily compounding generates $512.67. If you are comparing regular recurring deposits, analyze compound growth streams with our annuity calculator.

Why banks use APR for loans and APY for deposits

Financial institutions understand marketing psychology and regulatory compliance:

• Savings and CDs: Banks promote APY because the compounding effect produces a higher number, making the deposit return appear more attractive to savers.
• Loans and Credit Cards: Lenders quote APR (or nominal rates) because excluding compounding produces a lower headline number, making borrowing appear less expensive.

For revolving credit card debt, compounding typically happens daily. A credit card with a 24.00% APR actually incurs an effective annual rate (APY) of 27.11% if the balance is carried across the entire year. To analyze fixed installment loans with scheduled payments, explore our EMI calculator or advanced loan calculator.

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