Daily Compound Interest Formula (2026): $10K at 5% = $10,513 in 1 Year

To calculate daily compound interest, use A = P × (1 + r/365)^(365 × t) when r is a nominal annual rate. For an APY quote, first convert it to the rate convention used by the account; APY is already effective and should not be compounded a second time. A $10,000 example at a stated 5% rate is illustrative—use the provider disclosure and account convention for a real projection.

Key takeaways

• Formula: A = P × (1 + r/365)^(365 × t), where P is principal, r is the annual rate (as a decimal), and t is years.
• Daily compounding produces an APY about 0.12–0.13 percentage points higher than APR at typical 4–5% rates.
• $10,000 at 5% APR compounded daily becomes $10,512.67 in one year — the extra $12.67 over simple interest is the compounding bonus.
• On $10,000 at 5% APR, daily compounding earns about $0.55 more per year than monthly compounding. Over 20 years, the gap is ~$25. Tiny.
• When comparing savings products, always compare APY to APY — APY already reflects the compounding frequency.
• For balances that change daily (deposits + withdrawals), banks compute daily interest as balance × (APR/365) for each day, then credit the sum at month-end.

The daily compound interest formula

The mathematical formula is: A = P × (1 + r/365)^(365 × t). Breaking it down: P is your starting principal, r is the annual rate as a decimal (5% = 0.05), 365 is the compounding periods per year, and t is the number of years. The exponent 365 × t represents the total number of compounding periods over the time horizon.

For continuous deposits (a savings account where you add money during the year), the math gets more complex — you use the future-value-of-annuity formula on top of the lump-sum formula. Most calculators (including ours) handle this automatically.

Worked example: $10,000 at 5% APR daily compounding

• Day 1 balance: $10,000.00
• Day 1 interest: $10,000 × (0.05 / 365) = $1.3699
• Day 2 balance: $10,001.37
• Day 2 interest: $10,001.37 × (0.05 / 365) = $1.3701
• End of year 1: $10,512.67
• End of year 5: $12,840.25
• End of year 10: $16,486.65

Compare this to the same $10,000 at simple interest (no compounding): year 1 = $10,500, year 5 = $12,500, year 10 = $15,000. The compounding gap widens every year — over a decade, daily compounding earns $1,486 more than simple interest on the same rate.

Daily vs monthly vs annual compounding — actual numbers

$10,000 at a flat 5% APR over different time horizons:

• 1 year: Annual $10,500 / Monthly $10,512 / Daily $10,513
• 5 years: Annual $12,763 / Monthly $12,834 / Daily $12,840
• 10 years: Annual $16,289 / Monthly $16,470 / Daily $16,487
• 20 years: Annual $26,533 / Monthly $27,126 / Daily $27,185

The total advantage of daily over annual compounding at 5%/20 years is about $652 on $10,000 — meaningful but not life-changing. The advantage of daily over monthly is ~$60 over 20 years — essentially noise. Focus on the rate, not the frequency.

When does daily compounding matter?

• High-yield savings accounts (HYSAs): terms vary by provider; confirm how the account calculates, accrues and credits interest
• Money market accounts: use the account disclosure rather than assuming a daily convention
• Certificates of Deposit (CDs): compounding and early-withdrawal terms vary by issuer and product
• Bank savings accounts: the rate, balance method and crediting schedule are set by the account terms
• Mortgages and auto loans: payment and interest conventions vary; read the note or loan agreement
• 401(k) and IRA balances: investment returns are market-based, while contributions and distributions follow the plan or custodial terms

How to use our calculator

Open the calculator, set compounding frequency to "Daily" (365 per year), enter your initial balance, the current provider rate and time horizon. The visual breakdown shows year-by-year growth and cumulative interest. For a HYSA, model the disclosed variable APY over the period and test a lower-rate case; for long-term investing, use a range of nominal or real return assumptions that match the asset.

Use the calculator at the bottom of this page or directly at our dedicated tool.

The mistake to avoid

Some calculators present "compound frequency" as the headline feature, implying you should optimize for daily vs continuous. This is misleading. The difference between daily and continuous compounding at 5% over 10 years is $0.10 on $10,000 — literally a dime. What matters is the APY itself, the principal, and the time. Always pick the higher-APY account, then ignore frequency.