Loan Payoff Calculator With Extra Payment

Loan Payoff Formula:

\[ n' = \frac{-\log\left(1 - \frac{P \times r}{M + E}\right)}{\log(1 + r)} \]

Principal (P):

USD

Interest Rate (r):

decimal

Monthly Payment (M):

USD

Extra Payment (E):

USD

Reduced Payments (n'):

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1. What is a Loan Payoff Calculator With Extra Payment?

Definition: This calculator determines how much faster you can pay off a loan by making extra payments.

Purpose: It helps borrowers understand the impact of additional payments on their loan term and interest savings.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ n' = \frac{-\log\left(1 - \frac{P \times r}{M + E}\right)}{\log(1 + r)} \]

Where:

\( n' \) — Reduced number of payments (unitless)
\( P \) — Principal loan amount (USD)
\( r \) — Monthly interest rate (decimal)
\( M \) — Regular monthly payment (USD)
\( E \) — Extra monthly payment (USD)

Explanation: The formula calculates how many payments would be needed when applying extra money toward the principal each month.

3. Importance of Extra Payment Calculation

Details: Making extra payments can significantly reduce the loan term and total interest paid, potentially saving thousands of dollars.

4. Using the Calculator

Tips: Enter the principal amount, monthly interest rate (as decimal), regular payment, and any extra amount you plan to pay. All values must be ≥ 0.

5. Frequently Asked Questions (FAQ)

Q1: How do I convert APR to monthly rate?
A: Divide your annual rate by 12 (e.g., 6% APR = 0.06/12 = 0.005 monthly rate).

Q2: Does this account for changing interest rates?
A: No, this assumes a fixed interest rate for the life of the loan.

Q3: What's the best way to apply extra payments?
A: Specify that extra payments should go toward principal, not future payments.

Q4: How much can I save with extra payments?
A: Even small extra payments can save significant interest and shorten your loan term.

Q5: What if my result shows more payments than original?
A: Check that your regular payment is sufficient to cover at least the interest (M > P×r).