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How to use the daily compound interest formula
Each day, interest is calculated on the balance so far, including interest added on earlier days. That is the key difference from simple interest, which is calculated only on the original principal. The Consumer Financial Protection Bureau defines compound interest as interest earned on savings and on the interest earned along the way (CFPB, reviewed October 19, 2023).
For a 365-day year, the formula is:
A = P(1 + r/365)365t
- A = ending balance, including principal and compounded interest
- P = starting principal
- r = nominal annual interest rate as a decimal; for example, 5% is 0.05
- t = time in years
- 365 = assumed number of daily compounding periods per year
If you know the number of days directly, use A = P(1 + r/365)d, where d is the number of days under the convention being used. Interest earned is A − P.
Example: $1,000 at 5% for 365 days
Assuming a constant 5% nominal annual rate, daily compounding, and no other account activity:
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A = 1,000(1 + 0.05/365)365 ≈ $1,051.27
The illustrative interest is therefore about $51.27, before any account-specific rounding or other terms. This is a mathematical example, not a promised account result.
APR, nominal rate, and APY are not interchangeable
The formula takes a nominal annual rate and divides it by 365 to calculate a daily rate. An APY is an annualized effective yield that already reflects compounding under the applicable calculation. Do not enter a quoted APY as though it were a nominal rate and compound it again. Check the rate label and the account disclosures.
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For U.S. deposit accounts, the CFPB’s Regulation DD Appendix A sets out APY calculation rules and examples that account for period lengths and actual days (Appendix A to Part 1030). Institutions that choose to compound or credit interest may use annual, semiannual, quarterly, monthly, daily, or another basis; federal rules do not impose one universal frequency (CFPB, § 1030.7).
The CFPB’s basic example illustrates annual—not daily—compounding: $1,000 at 5% grows to $1,050 after the first year and $1,102.50 after the second. Those figures should not be mistaken for the result of the daily formula.
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Why an account’s actual result may differ
Savings and other deposit accounts
The formula is an estimate for a stable rate, a specified day-count convention, and an unchanged balance apart from interest. Actual rates may change, deposits and withdrawals change the balance path, and day counts, posting practices, rounding, and account terms can affect the result. Regulation DD’s APY examples use actual days in relevant calculations, so a simple 365-day model may not reproduce an account disclosure exactly.
For example, the CFPB’s current Appendix A illustrates a specific six-month calculation using $1,000 at 5% daily compounding over adjacent periods of 91 and 92 days. Its stated total interest is $26.68 and its APY is 5.39%. Those numbers belong to that regulatory example; they are not a general forecast for every six-month period or account.
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Credit cards
A credit card’s daily periodic rate is not, by itself, a complete description of how interest accrues. The CFPB describes daily periodic rates on its page as APR divided by 365 for the methods discussed. Under the daily-balance method with compounding, prior-day interest is added to the next day’s balance; under the described method without compounding, unpaid finance charges are excluded from the next daily balance. Check the card agreement and billing method rather than assuming every card uses the same daily calculation (CFPB, Credit card contract definitions).
Statement-period APY
APY shown for a periodic statement is not simply the future-value calculation for one fixed principal. The Federal Reserve describes APY earned for periodic statements as an annualized relationship between interest actually earned and average daily balance, with a special formula for certain daily-balance methods (Federal Reserve, Part II).
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What to check when estimating real account growth
- Whether the quoted figure is a nominal annual rate or APY
- How often interest is compounded and credited
- Whether the rate is fixed or variable
- Which day-count and statement-period methods apply
- Whether fees or minimum-balance requirements affect the balance
- Whether planned deposits or withdrawals change the amount on which interest is calculated
For a quick estimate, use the formula with the stated assumptions. For an exact account figure, use the institution’s disclosures or calculation method; the applicable terms determine the result.
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