Hong Life CalculatorsUnderstanding the daily compound interest calculator — concept and principle
Daily compounding means interest is worked out every day and added to the balance, so tomorrow's interest is earned on today's interest too. This calculator projects a savings balance with a starting amount, a fixed deposit every day and an annual rate compounded daily. It suits high-yield savings accounts, money-market funds and daily saving habits.
How it is calculated
- Daily rate: r = annual rate ÷ 365.
- Each day: balance = balance × (1 + r) + daily contribution.
- Total contributed = starting amount + contribution × days; interest = final balance − total contributed.
- Effective annual rate (EAR) = (1 + r)³⁶⁵ − 1.
The contribution is added at the end of each day, so it begins earning interest the next day. Taxes and fees are not included.
The principle
Compounding is repeated multiplication. After n days a single deposit grows to P × (1 + r)ⁿ, and each later deposit grows the same way for the days it has left. The more often interest is credited, the higher the effective rate, but the gain shrinks quickly: yearly, monthly and daily compounding at 5% give 5%, 5.116% and 5.127%, and the limit, continuous compounding, gives e^0.05 − 1 ≈ 5.127%. So daily compounding is almost the maximum possible.
Worked example
- Inputs: starting amount $10,000, $10 a day, 5% a year, 365 days.
- Daily rate: 0.05 ÷ 365 ≈ 0.000137.
- The starting amount alone grows to 10,000 × (1 + r)³⁶⁵ ≈ $10,512.67.
- Repeating the daily step 365 times gives a final balance of $14,255.20.
- Contributed: 10,000 + 10 × 365 = $13,650.00, so interest = $605.20.
- EAR: (1 + 0.05/365)³⁶⁵ − 1 = 5.127%.
Of the interest, about $512.67 comes from the starting amount and $92.53 from the daily deposits, which are in the account for half the year on average.
How to read the result
Compare accounts by EAR (often shown as APY), not by the nominal rate, because it already includes compounding. In the first year interest is small next to your deposits; only over many years does it become the larger part.
Common mistakes
- Expecting daily compounding to double returns. At normal rates it adds only about 0.01 percentage point over monthly compounding.
- Ignoring tax on interest, which lowers the real gain.
- Assuming the rate stays fixed. Savings rates follow central-bank rates and can change at any time.
Frequently asked questions
Does daily compounding mean interest is paid every day?
Not always. Many accounts accrue interest daily but pay it into the account monthly, which gives almost the same result.
What is the difference between APR and APY?
APR is the nominal yearly rate; APY (or EAR) includes the effect of compounding. At 5% compounded daily, APY is 5.127%.
How do I compound for a whole year without contributions?
Multiply the deposit by (1 + rate ÷ 365)³⁶⁵. For $10,000 at 5% that is about $10,512.67.
Sources: U.S. Truth in Savings Act, Regulation DD (12 CFR Part 1030), annual percentage yield · S. A. Ross, R. W. Westerfield, B. D. Jordan, Fundamentals of Corporate Finance, McGraw-Hill (compounding and effective annual rate)