Loan Amortization Calculator Compound Daily Formula

Daily Compound Amortization Formula:

\[ PMT = P \times \frac{r \times (1 + r)^n}{(1 + r)^n - 1} \]

where \( r = \frac{annual\_rate}{365} \)

Daily Payment (PMT):

Total Payment:

Total Interest:

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1. What is Daily Compound Amortization?

Daily compound amortization calculates loan payments where interest is compounded daily. This method provides a more accurate calculation of interest for loans that accrue interest on a daily basis, such as credit cards or some short-term loans.

2. How Does the Calculator Work?

The calculator uses the daily compound amortization formula:

\[ PMT = P \times \frac{r \times (1 + r)^n}{(1 + r)^n - 1} \]

where \( r = \frac{annual\_rate}{365} \)

Where:

\( PMT \) — Daily payment amount
\( P \) — Principal loan amount
\( r \) — Daily interest rate (annual rate divided by 365)
\( n \) — Total number of days in loan term

Explanation: The formula accounts for the effect of daily compounding, where each day's interest is added to the principal for the next day's interest calculation.

3. Importance of Daily Compounding

Details: Daily compounding can significantly affect the total interest paid, especially for loans with higher interest rates or longer terms. It provides a more precise calculation than monthly compounding for daily-accruing loans.

4. Using the Calculator

Tips: Enter the principal amount in dollars, annual interest rate as a percentage (e.g., 5.25 for 5.25%), and loan term in days. 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 it once per month. Daily compounding typically results in slightly higher total interest.

Q2: What types of loans use daily compounding?
A: Credit cards, payday loans, and some personal loans often use daily compounding. Mortgages and auto loans typically use monthly compounding.

Q3: Why divide the annual rate by 365?
A: This converts the annual rate to a daily rate, which is necessary for daily compounding calculations.

Q4: How accurate is this calculator for leap years?
A: The calculator uses 365 days for simplicity. For exact calculations in leap years, you might use 366 days for those specific years.

Q5: Can I use this for loans with different compounding periods?
A: This calculator is specifically designed for daily compounding. For monthly or quarterly compounding, different formulas would be needed.