Daily Compound Interest
Daily compounding means interest is calculated and added to the balance each day. The next day's calculation then uses the updated balance, so previously credited interest can itself earn interest. This calculator is useful for comparing daily compounding with monthly or annual compounding and for understanding the effect of frequent crediting.
Quick Answer
For daily compounding, a common formula is A = P(1 + r/365)365t, where P is principal, r is the annual rate as a decimal, and t is time in years. Some financial products use a different day-count convention, so the actual account terms should always be checked.
Understanding the Inputs
P is the starting balance. r is the annual rate, so 5% becomes 0.05. 365 represents daily compounding in the standard formula. t is the number of years. If the calculator includes deposits or withdrawals, those are additional cash flows rather than part of the basic formula.
How to Use the Calculator
- Enter the starting amount.
- Enter the annual interest rate.
- Enter the number of years.
- Review the final balance and the interest portion.
Worked Examples
Example 1: $1,000 at 5% for 1 year with daily compounding gives approximately $1,051.27.
Example 2: $5,000 at 6% for 3 years with daily compounding grows to approximately $5,986.55.
Example 3: $10,000 at 4% for 10 years with daily compounding gives approximately $14,918.25. The exact figure can vary when a financial institution uses a specific day-count method or rate convention.
Daily vs Annual Compounding
| Principal | Rate | Time | Annual Compounding | Daily Compounding |
|---|---|---|---|---|
| $1,000 | 5% | 1 year | $1,050.00 | ~$1,051.27 |
| $5,000 | 6% | 3 years | ~$5,955.08 | ~$5,986.55 |
| $10,000 | 4% | 10 years | $14,802.44 | ~$14,918.25 |
What Daily Compounding Does Not Tell You
A mathematical daily-compound result does not automatically represent the amount you will receive from a real bank or investment. Accounts can use variable rates, different day-count conventions, minimum balances, fees, taxes, or other conditions. For credit products, the advertised APR may also be applied according to specific account rules.
Common Mistakes
- Entering a percentage as 5 instead of 0.05 when a decimal is required.
- Assuming every account uses exactly 365 compounding periods.
- Comparing rates without checking whether they are nominal or effective rates.
- Forgetting additional deposits or withdrawals when estimating a real balance.