How to Calculate Daily Compound Interest on a Loan

Daily Compound Interest Formula:

\[ I_{daily} = P \times \frac{r}{365} \] \[ A = P \times \left(1 + \frac{r}{365}\right)^{365 \times t} \]

Daily Interest (I_daily):

Future Value (A):

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1. What is Daily Compound Interest?

Daily compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods, compounded on a daily basis. This results in faster growth of your loan balance compared to simple interest or less frequent compounding.

2. How Does the Calculator Work?

The calculator uses the daily compound interest formulas:

\[ I_{daily} = P \times \frac{r}{365} \] \[ A = P \times \left(1 + \frac{r}{365}\right)^{365 \times t} \]

Where:

\( I_{daily} \) — Daily interest amount
\( P \) — Principal loan amount
\( r \) — Annual interest rate (in decimal form)
\( A \) — Future value of the loan
\( t \) — Time period in years

Explanation: The first formula calculates the daily interest amount, while the second formula calculates the total future value of the loan including all compounded interest.

3. Importance of Daily Compounding

Details: Daily compounding can significantly increase the total interest paid on a loan over time. Understanding this compounding effect is crucial for borrowers to make informed financial decisions and accurately estimate their repayment obligations.

4. Using the Calculator

Tips: Enter the principal amount in dollars, annual interest rate as a percentage (e.g., 5 for 5%), and time period 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 calculates interest once per month. Daily compounding results in slightly higher total interest due to more frequent compounding periods.

Q2: Is daily compounding common for loans?
A: While not as common as monthly compounding, some loans (particularly certain types of credit cards and short-term loans) use daily compounding to calculate interest.

Q3: How does the time period affect the calculation?
A: The longer the time period, the more significant the effect of compounding becomes. Small daily interest amounts can accumulate substantially over extended periods.

Q4: Can this calculator be used for savings accounts?
A: Yes, the same formulas apply to savings accounts with daily compounding, though the context changes from paying interest to earning interest.

Q5: What's the difference between APR and APY with daily compounding?
A: APR (Annual Percentage Rate) doesn't account for compounding, while APY (Annual Percentage Yield) does. With daily compounding, APY will be slightly higher than APR due to the compounding effect.