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.
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.
How does daily compounding work with crypto staking?
Cryptocurrency staking rewards are often quoted as annual percentage rates, but many protocols distribute rewards daily or even per block (every few seconds). When staking rewards are automatically restaked (auto-compounding), the effect is equivalent to daily compound interest but potentially even more powerful since compounding can occur thousands of times per day. For example, an advertised 8% APR staking reward with daily auto-compounding yields an effective APY of approximately 8.33%. Some DeFi yield farming protocols advertise extremely high APRs of 100-1000%, and the difference between APR and APY becomes dramatic at these levels. A 365% APR with daily compounding produces an APY of approximately 3,678%, meaning $1,000 would theoretically grow to $37,780 in one year, though such high rates are rarely sustainable.
How much does $10,000 earn with daily compounding at different rates?
Here are the exact earnings for $10,000 over one year with daily compounding at various rates. At 1% APR, you earn $100.50 (APY 1.005%). At 2% APR, you earn $201.99 (APY 2.020%). At 3%, you earn $304.52 (APY 3.045%). At 4%, you earn $408.08 (APY 4.081%). At 5%, you earn $512.67 (APY 5.127%). At 7%, you earn $725.00 (APY 7.250%). At 10%, you earn $1,051.56 (APY 10.516%). At 15%, you earn $1,617.98 (APY 16.180%). Over longer periods the differences compound dramatically. At 5% daily compounding over 10 years, $10,000 grows to $16,486.65, while at 10% it grows to $27,179.10, nearly triple the 5% result despite only double the rate.