Amortization Calculator With Extra Payments

Amortization Formula with Extra Payments:

\[ B = P \times \frac{(1 + r)^n - (1 + r)^p}{(1 + r)^n - 1} \text{ adjusted for extra payments} \]

Principal Amount (P):

Interest Rate (r):

Loan Term (n):

months

Months Paid (p):

months

Extra Payments:

Remaining Loan Balance:

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1. What is Amortization with Extra Payments?

Amortization is the process of spreading out a loan into fixed payments over time. Extra payments reduce the principal faster, saving interest and shortening the loan term.

2. How Does the Calculator Work?

The calculator uses the amortization formula with extra payments adjustment:

\[ B = P \times \frac{(1 + r)^n - (1 + r)^p}{(1 + r)^n - 1} \text{ adjusted for extra payments} \]

Where:

$ B $ — Remaining balance
$ P $ — Principal loan amount
$ r $ — Monthly interest rate (annual rate ÷ 12)
$ n $ — Total number of payments (term in months)
$ p $ — Number of payments already made
Extra payments — Additional principal payments made

Explanation: The formula calculates the remaining balance after p payments, then subtracts the total extra payments made.

3. Importance of Extra Payments

Details: Making extra payments can significantly reduce total interest paid and shorten the loan term. Even small regular extra payments can have a large impact over time.

4. Using the Calculator

Tips: Enter the original loan amount, annual interest rate, loan term in months, number of payments already made, and any extra payments. All values must be valid (principal > 0, rate ≥ 0, term > 0).

5. Frequently Asked Questions (FAQ)

Q1: How much can extra payments save?
A: Depends on loan size, rate, and payment amount. A $100 extra monthly payment on a $200,000 loan at 4% can save ~$26,000 and shorten term by 5 years.

Q2: Should I pay extra principal or refinance?
A: Depends on rates and fees. If current rate is low, extra payments may be better than refinancing with closing costs.

Q3: When is the best time to make extra payments?
A: Earlier in the loan term has greatest impact as more payment goes toward interest later.

Q4: Are there prepayment penalties?
A: Most modern loans don't have them, but check your loan agreement.

Q5: How to maximize extra payment impact?
A: Apply payments directly to principal, make payments biweekly instead of monthly, or make one extra payment per year.