Daily compound interest formula
The daily compound interest formula is A = P(1 + r/365)365t for an annual rate r, or A = P(1 + d)days for a daily rate d. It is the general compound interest formula with n = 365.[1]
A savings account paying 4.5% compounded daily: 10,000 × (1 + 0.045/365)365 = $10,460.25, an APY of 4.602%. Regulation DD lets banks credit interest using the daily balance method, applying a daily periodic rate to the full balance each day, and requires the result to be disclosed as an APY.[3][2]
Daily vs monthly compounding on savings
For a savings account, compounding daily instead of monthly adds only a few dollars a year. $10,000 at 4.5%:
| Time | Compounded daily | Compounded monthly | Daily earns more by |
|---|---|---|---|
| 1 year | $10,460.25 | $10,459.40 | $0.85 |
| 5 years | $12,523.05 | $12,517.96 | $5.10 |
| 10 years | $15,682.69 | $15,669.93 | $12.76 |
Compare accounts by APY, not by how often they compound; the APY calculator converts any rate. The compound interest calculator adds monthly deposits, inflation and goal seek.
Compounding a daily rate: weekdays only
Skipping weekends cuts a 30-day run to 22 compounding days. At 1% a day, $1,000 becomes $1,347.85 when every day counts and $1,244.72 on weekdays only. Choose "Weekdays only" when returns accrue on trading or business days.
The reinvestment setting splits each day's earnings: at 100% everything compounds; at 50% half is paid out and only half stays in the balance, so the balance grows more slowly while the payouts add up separately in the table.
What a daily rate means over a year
Small daily rates compound into enormous yearly ones. 1% a day for 365 days turns $1,000 into $37,783, an annual return of 3,678%. No savings account, CD or Treasury security pays anything close to that.
Promised daily returns are a warning signThe SEC warns that an investment program promising high returns with little or no risk is likely a fraud.[4] Use this calculator for arithmetic, not as evidence that a promised daily return is real.
Daily interest on a balance
Daily interest at an annual rate is balance × rate ÷ 365. $10,000 at 4.5% earns about $1.23 a day before compounding. For interest per day, month and year at several balances, see how much interest will I earn.
Related calculators
- Compound interest calculatorDeposits, any compounding, inflation, goal seek, chart and CSV
- APY calculatorAPR to APY and back, for any compounding
- How much interest will I earn?Interest per day, month and year on any balance, with tables
- High yield savings account calculatorYour APY against the FDIC national average, in dollars
Frequently asked questions
How do you calculate daily compound interest?
Divide the annual rate by 365, add 1, raise it to the number of days and multiply by the balance: A = P(1 + r/365)days. $10,000 at 4.5% for a year gives $10,460.25.
How much is 1% daily compound interest over 30 days?
$1,000 × 1.0130 = $1,347.85, a gain of 34.8%. On weekdays only (22 days) it is $1,244.72.
Is interest compounded daily better than monthly?
Yes, but only slightly: at 4.5%, daily compounding raises the APY by about 0.01 percentage point over monthly. The quoted rate matters much more.
Do banks compound interest daily?
Many do. Regulation DD allows the daily balance method, and banks must show the result as an APY so accounts with different compounding can be compared.