Compound Daily Interest Calculator
Calculate compound interest with daily compounding for savings and crypto staking. Enter values for instant results with step-by-step formulas.
Reviewed by Sahil, Senior Finance & Tax Editor
Formula
FV = P x (1 + r/365)^d + C x [(1 + r/365)^d - 1] / (r/365)
Where FV = Future Value, P = Principal (initial amount), r = Annual interest rate (as decimal), d = Number of days, and C = Daily contribution amount. The daily rate is the annual rate divided by 365. The first term calculates growth of the principal and the second term calculates growth from daily contributions.
Worked Examples
Example 1: High-Yield Savings Account
Problem:Deposit $10,000 in a high-yield savings account at 4.75% APR compounded daily for 2 years. No additional contributions.
Solution:Daily rate = 4.75% / 365 = 0.013014% per day\nDays = 2 x 365 = 730 days\nFV = $10,000 x (1 + 0.0001301)^730\nFV = $10,000 x 1.09972\nFV = $10,997.20\nInterest earned = $10,997.20 - $10,000 = $997.20\nEffective APY = (1 + 0.0475/365)^365 - 1 = 4.864%\nGrowth multiple = 1.0997x
Result:Future Value: $10,997.20 | Interest: $997.20 | Effective APY: 4.864%
Example 2: Daily DCA into Staking Rewards
Problem:Start with $5,000 and contribute $10/day into a crypto staking protocol earning 8% APR compounded daily for 1 year.
Solution:Daily rate = 8% / 365 = 0.02192% per day\nFV of principal = $5,000 x (1.0002192)^365 = $5,416.39\nFV of $10/day contributions = $10 x ((1.0002192^365 - 1) / 0.0002192) = $3,803.91\nTotal FV = $5,416.39 + $3,803.91 = $9,220.30\nTotal contributed = $5,000 + $10 x 365 = $8,650\nInterest earned = $9,220.30 - $8,650 = $570.30\nEffective APY = 8.328%
Result:Future Value: $9,220.30 | Contributed: $8,650 | Interest: $570.30 | APY: 8.328%
Frequently Asked Questions
What is daily compound interest and how does it differ from monthly compounding?
Daily compound interest calculates and adds earned interest to your balance every single day, rather than once per month or once per year. With daily compounding, the interest earned on day 1 starts earning its own interest on day 2, creating a slightly faster snowball effect compared to monthly compounding. For example, $10,000 at 5% annual interest compounded daily produces $512.67 in one year, while monthly compounding produces $511.62, a difference of $1.05. The difference becomes more significant with higher interest rates and longer time periods. At 10% over 10 years, the difference between daily and monthly compounding on $10,000 is approximately $45. Most high-yield savings accounts and money market funds compound interest daily.
How is daily compound interest calculated?
Daily compound interest uses the formula FV = P x (1 + r/365) raised to the power of the number of days, where P is the principal, r is the annual interest rate as a decimal, and 365 represents the number of days in a year. The daily rate is simply the annual rate divided by 365. For a $10,000 deposit at 5% annual interest, the daily rate is 0.05/365 = 0.00013699. After day 1, the balance becomes $10,000 x 1.00013699 = $10,001.37. After day 2, it becomes $10,001.37 x 1.00013699 = $10,002.74, and so on. Each day the base amount grows slightly, so the dollar amount of interest earned increases every single day even though the rate stays constant.
What investments use daily compounding?
Several common financial products use daily compounding to calculate returns. High-yield savings accounts at online banks typically compound interest daily and credit it monthly, which is why they advertise both the nominal rate and the higher APY (Annual Percentage Yield). Money market accounts and money market funds also frequently compound daily. Certificate of deposit (CD) interest is commonly compounded daily, though some institutions use monthly compounding. Cryptocurrency staking and DeFi lending protocols often compound rewards daily or even more frequently, sometimes every few seconds with automatic compounding. Credit card interest also compounds daily, which is why carrying a balance is so expensive. Treasury bonds and most corporate bonds do not compound daily since they pay interest on fixed schedules.
What is the difference between APR and APY with daily compounding?
APR (Annual Percentage Rate) is the stated nominal interest rate without accounting for compounding effects. APY (Annual Percentage Yield) is the actual effective annual return after daily compounding is factored in. With daily compounding, the APY is always higher than the APR. For example, a 5.00% APR compounded daily produces an APY of 5.127%, meaning you actually earn 5.127% on your money over a full year. At 10% APR, the daily-compounded APY is 10.516%. The formula for converting is APY = (1 + APR/365) raised to the 365th power, minus 1. When comparing savings accounts or CDs from different banks, always compare APY values rather than APR because APY gives you the true apples-to-apples comparison of how much interest you will actually earn.
References
Reviewed by Sahil, Senior Finance & Tax Editor · Editorial policy