Loan Amortization Calculator Compound Daily Interest

Loan Amortization Formula:

\[ PMT = P \times \frac{r \times (1 + r)^n}{(1 + r)^n - 1} \] \[ \text{where } r = (1 + \frac{annual\_rate}{365})^{\frac{1}{12}} - 1 \]

Monthly Payment (PMT):

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1. What is Loan Amortization with Daily Compounding?

This calculator determines the fixed monthly payment (PMT) needed to pay off a loan with daily compounding interest over a set period. It accounts for the fact that interest accrues daily but payments are made monthly.

2. How Does the Calculator Work?

The calculator uses the loan amortization formula:

\[ PMT = P \times \frac{r \times (1 + r)^n}{(1 + r)^n - 1} \] \[ \text{where } r = (1 + \frac{annual\_rate}{365})^{\frac{1}{12}} - 1 \]

Where:

$ P $ — Principal loan amount ($)
$ r $ — Monthly interest rate (calculated from daily compounding)
$ n $ — Number of monthly payments
$ annual\_rate $ — Annual interest rate in decimal form

Explanation: The formula accounts for daily compounding by converting the annual rate to a daily rate, then calculating the effective monthly rate.

3. Importance of Accurate Loan Calculation

Details: Understanding your exact monthly payment helps with budgeting and shows how much interest you'll pay over the loan's life. Daily compounding typically results in slightly higher payments than monthly compounding.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Why use daily compounding instead of monthly?
A: Many loans (especially credit cards and some mortgages) compound interest daily, which can result in slightly higher payments than monthly compounding.

Q2: How does loan term affect payments?
A: Longer terms reduce monthly payments but increase total interest paid. Shorter terms have higher payments but lower total interest.

Q3: What's the difference between APR and interest rate?
A: APR includes fees and other loan costs, while the interest rate is just the cost of borrowing the principal.

Q4: Are there limitations to this calculation?
A: This assumes fixed rates and equal payments. Adjustable-rate loans or loans with balloon payments require different calculations.

Q5: How can I pay less interest overall?
A: Make additional principal payments when possible, choose shorter loan terms, or negotiate lower interest rates.