Daily Compound Interest Calculator

Daily Compound Interest Formula:

\[ FV = P \times (1 + \frac{r}{365})^{365 \times t} \]

Future Value (FV):

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1. What is Daily Compound Interest?

Daily compound interest means that interest is calculated and added to the principal every day, leading to exponential growth of your investment over time.

2. How Does the Calculator Work?

The calculator uses the daily compound interest formula:

\[ FV = P \times (1 + \frac{r}{365})^{365 \times t} \]

Where:

\( FV \) — Future value of the investment
\( P \) — Principal investment amount
\( r \) — Annual interest rate (in decimal form)
\( t \) — Time the money is invested for (in years)
365 — Number of compounding periods per year

Explanation: The formula accounts for interest being calculated and added to the principal balance each day, leading to "interest on interest" effects.

3. Importance of Daily Compounding

Details: Daily compounding can significantly increase investment returns compared to annual or monthly compounding, especially over long periods. This is the most frequent compounding schedule commonly available.

4. Using the Calculator

Tips: Enter the principal amount in USD, annual interest rate as a decimal (e.g., 0.05 for 5%), and time in years. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: How does daily compounding differ from monthly compounding?
A: Daily compounding calculates interest every day, while monthly compounding does it once per month. Daily compounding yields slightly higher returns.

Q2: What's the difference between APR and APY with daily compounding?
A: APR is the annual rate, while APY (Annual Percentage Yield) accounts for compounding effects. APY will be higher than APR when interest compounds.

Q3: How accurate is this calculator for real-world investments?
A: It provides a good estimate, but actual returns may vary due to factors like changing interest rates, fees, or different day-count conventions.

Q4: Can I use this for debt calculations?
A: Yes, the same formula applies to debt that compounds daily, though you'd want to minimize this type of debt due to rapid growth.

Q5: Why is the rate input as a decimal?
A: Mathematical formulas typically use decimal form (0.05 for 5%). To input a percentage, simply divide by 100 (e.g., 5% becomes 0.05).