How to Calculate Daily Compound Interest: Formula, Examples & HYSA Math
Daily compound interest formula: A = P × (1 + r/365)^(365×t). Worked examples for HYSAs at 5% APY, CDs, and money market accounts. Free calculator included.
Interest calculated and added to the balance every day, so each day's interest is computed on a slightly larger balance than the day before.
Example: A $10,000 HYSA at 5% APR compounded daily earns about $1.37 per day initially, rising slightly each day as the balance grows.
The effective annual rate of return after accounting for compounding. For daily compounding, APY is always slightly higher than the stated APR.
Example: A 5.00% APR with daily compounding produces a 5.127% APY — that 0.127% is the compounding bonus.
The simple yearly interest rate before compounding is applied. Used on loans (legally required) but less useful for comparing savings accounts than APY.
Example: Two HYSAs advertised at "5.00% APR" with different compounding frequencies actually yield slightly different real returns. Always compare APY to APY.
Daily compound interest is the standard for cash savings accounts in the United States — high-yield savings accounts (HYSAs), most CDs, and money market accounts all compound daily. This guide walks through the formula, gives concrete examples at typical 4–5% HYSA rates, and explains the difference vs monthly or annual compounding so you can compare any savings product correctly.
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): all major US HYSAs compound daily — Marcus, Ally, Discover, SoFi, Capital One 360
- Money market accounts: nearly all compound daily
- Certificates of Deposit (CDs): most compound daily, some compound monthly
- Bank savings accounts: most credit interest daily, compound monthly
- Mortgages and auto loans: typically NOT daily — most amortize monthly
- 401(k) and IRA balances: monthly compounding by convention, since contributions happen monthly
How to use our calculator
Open the calculator, set compounding frequency to "Daily" (365 per year), enter your initial balance, expected annual rate, and time horizon. The visual breakdown shows year-by-year growth and the cumulative interest earned. For HYSA modeling at 4–5% APY over 1–5 years, this is the most accurate tool. For long-term investing in index funds, switch to monthly compounding at 7–10%.
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.
Daily compounding across rates and time
$10,000 lump sum compounded daily at different rates, shown as future value:
| Dimension | Rate (APR) | 1 year | 5 years | 10 years | 20 years |
|---|---|---|---|---|---|
| 3% (low HYSA) | $10,305 | $11,618 | $13,498 | $18,221 | |
| 4% (typical HYSA 2024) | $10,408 | $12,213 | $14,917 | $22,252 | |
| 5% (top HYSA 2024) | $10,513 | $12,840 | $16,487 | $27,185 | |
| 7% (S&P avg real) | $10,725 | $14,189 | $20,132 | $40,529 | |
| 10% (S&P avg nominal) | $11,052 | $16,486 | $27,179 | $73,872 |
Frequently asked questions
How do I calculate daily compound interest by hand?
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Why don't all banks compound daily?
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Is daily compounding always better than monthly?
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How is daily interest credited?
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Does daily compounding work the same on debt?
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Plug in your own amounts with our free calculators.