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Finance Calc Kit
Investments

Compound Daily Interest Calculator

Calculate the growth of your investments or savings with daily compound interest. See the impact of daily compounding over time with detailed charts and tables.

Investment parameters

$
%
Popular interest rates:
Common investment periods:

Periodic contributions (Optional)

Total Ending Balance

$12,840.03

Includes $2,840.03 compound interest earned at 5.127% APY

Total Principal
$10,000.00
Total Interest
$2,840.03
Effective APY
5.127%
Daily Rate
0.0137%

Growth breakdown after 5 years

  • Initial Principal$10,000.0077.9%
  • Compound Interest Earned$2,840.0322.1%

Daily compounding vs other frequencies

Compare how daily compounding outperforms other compounding frequencies on a 5.00% nominal rate over 5 years.

FrequencyPeriods/YrEffective APYTotal InterestFinal Balance
Daily (365/yr)This Calculator3655.127%$2,840.03$12,840.03
Monthly (12/yr)125.116%$2,833.59$12,833.59
Quarterly (4/yr)45.095%$2,820.37$12,820.37
Semi-Annually (2/yr)25.062%$2,800.85$12,800.85
Annually (1/yr)15.000%$2,762.82$12,762.82

Year-by-year compounding schedule

Detailed annual progression of daily interest accumulation and balance growth.

YearStarting BalanceInterest EarnedTotal InterestEnding Balance
Year 1$10,000.00+$512.67$512.67$10,512.67
Year 2$10,512.67+$538.96$1,051.63$11,051.63
Year 3$11,051.63+$566.59$1,618.22$11,618.22
Year 4$11,618.22+$595.64$2,213.86$12,213.86
Year 5$12,213.86+$626.17$2,840.03$12,840.03

How daily compound interest is calculated

Daily compounding calculates interest every single day, immediately adding it to your balance so the next day earns interest on that new interest.

  1. Convert annual nominal rate to daily rate

    rdaily=rnr_{\text{daily}} = \frac{r}{n}

    Divide the nominal annual rate of 5.00% by 365 days per year to get a daily rate of 0.01370% per day.

  2. Calculate effective Annual Percentage Yield (APY)

    APY=(1+rn)n−1\mathrm{APY} = \left(1 + \frac{r}{n}\right)^{n} - 1

    Compounding 365 times per year produces an effective yield of 5.127%, earning more than simple annual interest.

  3. Apply the daily compound interest formula

    A=P×(1+rn)n×tA = P \times \left(1 + \frac{r}{n}\right)^{n \times t}

    Over 5 years (1825 daily periods), an initial deposit of $10,000.00 compounds to $12,840.03, generating $2,840.03 in total interest earned.

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How daily compound interest works

Daily compound interest is one of the most powerful wealth-building mechanisms in personal finance. When an account compounds daily, the financial institution calculates interest every single day based on your current principal plus all previously accumulated interest. That day's interest is added to your balance, meaning tomorrow's interest is calculated on a slightly larger amount.

Over short time horizons, the difference between daily compounding and monthly compounding may appear modest. However, over multi-year periods or with large account balances, daily compounding produces substantial incremental returns. High-yield savings accounts, money market funds, and modern fintech cash management accounts frequently use daily compounding to maximize depositor returns.

To evaluate the effective annual rate across different compounding frequencies, use our APY calculator or convert stated loan rates using the APR to APY calculator. For standard periodic compounding with optional monthly contributions, use our compound interest calculator. If you are comparing fixed-term deposit products, explore our CD calculator and CD rate calculator, analyze generalized portfolio trajectories with the compound growth calculator, or calculate multi-year geometric growth rates with the CAGR calculator.

Daily compound interest mathematical formula

The standard mathematical formula for daily compound interest on a lump-sum deposit is expressed as:

A=P×(1+rn)n×tA = P \times \left(1 + \frac{r}{n}\right)^{n \times t}

Where:

  • AA is the final ending balance (future value).
  • PP is the initial principal deposit.
  • rr is the stated annual nominal interest rate in decimal form (for instance, 0.05 for 5.00%).
  • nn is the number of compounding cycles per calendar year (typically 365 for daily compounding, or 360 for commercial bank conventions).
  • tt is the total time the money is invested, measured in years.

Effective Annual Percentage Yield (APY)

Because interest compounds 365 times throughout the year, the effective annual return (APY) is higher than the stated nominal interest rate (rr):

APY=(1+r365)365−1\text{APY} = \left(1 + \frac{r}{365}\right)^{365} - 1

Formulas with periodic regular deposits

When regular contributions (PMT\text{PMT}) are added alongside initial principal, the future value combines the lump-sum growth with the future value of an annuity compounded daily:

Atotal=P(1+rn)n×t+PMT×[(1+rn)n×t−1r/n]×(1+rn)timingA_{\text{total}} = P \left(1 + \frac{r}{n}\right)^{n \times t} + \text{PMT} \times \left[ \frac{\left(1 + \frac{r}{n}\right)^{n \times t} - 1}{r / n} \right] \times \left(1 + \frac{r}{n}\right)^{\text{timing}}

Where timing=1\text{timing} = 1 if deposits occur at the beginning of each period, or timing=0\text{timing} = 0 if deposits occur at the end of each period.

Published worked example

Suppose you deposit $10,000 into a high-yield savings account that pays a 6.00% nominal annual interest rate (r=0.06r = 0.06) compounded daily (n=365n = 365) over a 5-year investment period (t=5t = 5).

Step-by-step mathematical breakdown

1. Calculate the daily periodic interest rate:

rdaily=0.06365≈0.00016438356(0.016438% per day)r_{\text{daily}} = \frac{0.06}{365} \approx 0.00016438356 \quad (0.016438\% \text{ per day})

2. Determine the effective annual yield (APY):

APY=(1+0.06365)365−1=(1.00016438356)365−1≈0.0618313(6.183%)\text{APY} = \left(1 + \frac{0.06}{365}\right)^{365} - 1 = (1.00016438356)^{365} - 1 \approx 0.0618313 \quad (6.183\%)

3. Calculate total compounding periods:

N=365×5=1,825 daily cyclesN = 365 \times 5 = 1{,}825 \text{ daily cycles}

4. Calculate the 5-year ending balance:

A=$10,000×(1.00016438356)1825=$10,000×1.3498255=$13,498.26A = \$10{,}000 \times (1.00016438356)^{1825} = \$10{,}000 \times 1.3498255 = \$13{,}498.26

5. Compute total compound interest earned:

Total Interest=$13,498.26−$10,000.00=$3,498.26\text{Total Interest} = \$13{,}498.26 - \$10{,}000.00 = \$3{,}498.26

Daily compounding vs other frequencies

To understand why compounding frequency matters, compare how that same $10,000 at 6.00% grows across different compounding schedules over 5 years:

Compounding FrequencyCycles / YearEffective APY5-Year Ending BalanceTotal Interest Earned
Daily (365 days)3656.183%$13,498.26$3,498.26
Monthly126.168%$13,488.50$3,488.50
Quarterly46.136%$13,468.55$3,468.55
Annually16.000%$13,382.26$3,382.26
Simple Interest (No compounding)06.000%$13,000.00$3,000.00

Daily compounding generates $498.26 more interest than simple non-compounding interest, and $116.00 more than annual compounding on a modest $10,000 principal.

365-day exact year vs 360-day bank convention

In consumer finance, most retail savings accounts and deposit products calculate interest on an exact 365-day calendar year (or 366 days during leap years). However, some commercial banks, corporate bond issuers, and short-term commercial money market products use the 360-day commercial year convention (also known as 30/360 or European method).

When a bank calculates daily interest using r/360r / 360 but credits interest over 365 actual days, the effective yield is slightly higher because each day's fraction is based on 1/360th rather than 1/365th. This calculator allows you to toggle between both conventions to verify the exact rules applied by your institution.

Frequently asked questions

What is the difference between daily compounding and daily crediting?
Daily compounding means interest is calculated and added to the principal balance every day to generate future interest. Daily crediting refers to when that interest is formally posted and made accessible in your account balance (most banks calculate interest daily but post/credit it to your account on the last business day of each month).
How does daily compound interest affect savings accounts?
With daily compound interest, your savings account balance grows faster because you earn interest on top of yesterday interest. This results in an effective Annual Percentage Yield (APY) that exceeds the nominal annual interest rate.
Is APY higher than APR on daily compounding accounts?
Yes. APY reflects the full compounding effect over an entire year. Because interest compounds every day (365 times per year), APY will always be strictly higher than the stated nominal interest rate or APR.
What is the exact formula for daily compound interest?
The formula is A = P * (1 + r/365)^(365 * t), where A is the final balance, P is the principal, r is the annual nominal interest rate in decimal form, and t is the number of years.
Do leap years affect daily compound interest calculations?
During a leap year with 366 days, banks using exact day count conventions will calculate daily interest across 366 days (dividing by 366 or 365 depending on their deposit account agreement terms). Over multi-year investment horizons, 365 days per year provides a standardized benchmark.
Why do some financial institutions use a 360-day year instead of 365 days?
The 360-day year (12 months of 30 days) is a historical commercial banking and bond market convention. When applied to daily deposit interest, using 360 days in the denominator slightly increases daily interest accrual over 365 calendar days.

Resources and references

The formulas and methods in this calculator were checked against these independent sources.