Daily Compound Interest: The Formula Banks Use

When a bank advertises "4.50% APY, compounded daily," they are telling you two things: the rate and the frequency. The frequency determines how fast your money multiplies.

The Daily Compound Interest Formula

A = P(1 + r/n)^(nt)

Where:

• A = final amount
• P = principal (starting amount)
• r = annual interest rate (as a decimal)
• n = number of compounding periods per year (365 for daily)
• t = number of years

Example: $10,000 at 5% compounded daily for 10 years:

A = 10,000(1 + 0.05/365)^(365 × 10) A = 10,000(1.000137)^3650 A = $16,486.65

Compare that to annual compounding: A = 10,000(1.05)^10 = $16,288.95

The daily compounding earned an extra $197.70. Not life-changing on $10,000, but the gap widens dramatically with larger balances and longer time horizons.

APR vs. APY: Why It Matters

APR (Annual Percentage Rate) is the stated rate without accounting for compounding frequency. This is what credit cards and loans quote.

APY (Annual Percentage Yield) is the effective annual rate after compounding. This is what savings accounts and CDs quote.

A savings account advertising 5.00% APR with daily compounding actually yields an APY of 5.13%. That 0.13% difference is the compounding premium.

The conversion formula:

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

When comparing two savings accounts, always compare APY, not APR. If one advertises 4.90% APY and another advertises 5.00% APR compounded monthly, the first account actually pays more.

Where Daily Compounding Works For You

• High-yield savings accounts: Most online banks compound daily. Your interest earns interest every 24 hours.
• Certificates of deposit: Most CDs compound daily, which is why the APY is always slightly higher than the stated rate.
• Money market accounts: Same daily compounding as savings accounts.

Where Daily Compounding Works Against You

• Credit card debt: Credit cards compound daily on your balance. A $5,000 balance at 24.99% APR compounded daily grows to $6,415 in one year if untouched. That daily compounding works in reverse when it is debt.
• Student loans (private): Many private student loans compound daily. Federal student loans use simple daily interest, which is slightly less aggressive.

The takeaway: earn daily compounding on your savings. Avoid it on your debt. Use our Compound Interest Calculator to model both scenarios.

Frequently Asked Questions

Does it matter if my bank compounds daily vs. monthly? On a $50,000 savings balance at 4.5%, daily compounding earns about $15 more per year than monthly compounding. On a $500,000 balance, that gap is $150. It adds up over time but is not the primary factor in choosing a bank. Focus on the APY, which already reflects the compounding frequency.

Can I get daily compound interest on my investments? Stock market returns do not technically compound daily because prices only change when the market is open. However, reinvested dividends and interest payments create a compounding effect. The S&P 500's long-term average return of ~10% assumes dividend reinvestment, which is the stock market's version of compounding.