Compound interest calculator by days
Calculate compound interest by days (daily compounding) for any number of days, weeks, months, or years. See exactly how HYSAs, CDs, and money market accounts grow. Formula A = P(1+r/365)^(365t) — defaults pre-set, change any input.
How does daily compound interest work?
Daily compound interest applies the formula A = P × (1 + r/365)365t where P is your starting principal, r is the annual interest rate as a decimal, t is the number of years, and 365 is the number of compounding periods per year. Each day, the bank calculates one day's worth of interest on yesterday's closing balance and adds it to your account. Tomorrow's interest is then calculated on the new, slightly larger balance — so interest earns interest from day one.
How to calculate it in three steps. First, divide your annual rate by 365 to get the daily rate: a 5% APY becomes 0.01370% per day. Second, raise (1 + daily rate) to the power of 365 × years to get the growth factor: at 5% for one year that's (1.0001370)365 = 1.0513. Third, multiply your principal by that growth factor: $10,000 × 1.0513 = $10,513.
The difference between daily and annual compounding at the same nominal rate is small but real: at 5% over one year on $10,000, daily compounding produces $10,513 while annual compounding produces only $10,500 — a $13 gap. Over thirty years, that gap widens to roughly $1,800 on the same starting balance because the slightly higher effective rate (APY 5.127% vs APR 5.000%) compounds across decades.
Key terms
- Daily compounding
- Interest computed and added every day; tomorrow earns on today's new balance.
- APY
- Effective annual rate after compounding. The number to compare across products.
- APR
- Nominal rate before compounding. 5.00% APR daily = 5.127% APY.
Why daily compounding is the standard for cash accounts
Banks compound daily on most savings products because it's both fairer to customers and operationally simple at scale. Each day, the bank computes balance × (APR / 365) and adds it to the running balance. At month-end, the accumulated daily interest is credited to your account as a single deposit. By regulation (Truth in Savings Act), banks must advertise APY — the effective rate after this daily compounding.
Daily vs monthly vs annual — actual numbers
$10,000 at 5% APR over 10 years:
- Annual compounding: $16,289 (APY 5.000%)
- Monthly compounding: $16,470 (APY 5.116%)
- Daily compounding: $16,486 (APY 5.127%)
- Continuous compounding: $16,487 (APY 5.127%)
The difference between annual and daily is about 1.2% over a decade. The difference between daily and continuous is essentially zero. Once you compound daily or faster, you've captured 99.99% of the available compounding benefit.
What this calculator is good for
- HYSA projections — model 4-5% APY over 1-5 years. See current rates in the HYSA shopper.
- CD ladder planning — compare 12, 24, 36, 60-month terms. Try the CD ladder builder.
- Money market funds — most credit interest daily.
- Short-term goal saving — emergency fund, down payment, wedding.
What this calculator is NOT for
Long-term investing in stocks. Equity returns aren't smooth or daily-compounded — they fluctuate wildly. For projections beyond 5 years, use our compound investment calculator with a long-term equity rate (~7-10%), or the monthly compound interest calculator.
The biggest compounding mistake
Obsessing over compounding frequency while ignoring the APY itself. A 4.5% HYSA compounded daily earns less than a 5.0% HYSA compounded monthly. Always compare APY to APY — that number already accounts for the compounding frequency. Convert any APR to its true APY with our APR to APY converter.
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FAQ
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Methodology & sources
Formula: A = P(1 + r/365)^(365t). APY conversion: (1 + APR/365)^365 − 1. Rates verified against current FDIC national average and top HYSA postings. Updated 2026-06-15. See our editorial standards.
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Why this calculator and not the others?
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