Mortgage Payoff Calculator Remaining Balance Formula

Remaining Balance Formula:

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

Principal (P):

Interest Rate (r):

decimal

Total Term (n):

months

Months Paid (p):

months

Remaining Balance (B):

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1. What is the Remaining Balance Formula?

The remaining balance formula calculates how much you still owe on your mortgage after making a certain number of payments. It accounts for the principal amount, interest rate, total loan term, and payments made.

2. How Does the Calculator Work?

The calculator uses the remaining balance formula:

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

Where:

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

Explanation: The formula calculates how much of the principal remains unpaid after a certain number of payments, accounting for compound interest.

3. Importance of Remaining Balance Calculation

Details: Knowing your remaining balance helps with refinancing decisions, planning extra payments, understanding equity, and preparing for payoff.

4. Using the Calculator

Tips: Enter principal in dollars, interest rate as a decimal (5% = 0.05), total term in months, and number of payments made. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

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

Q2: Does this include taxes and insurance?
A: No, this calculates only the principal and interest portion of your mortgage.

Q3: How accurate is this calculation?
A: It's mathematically precise for fixed-rate mortgages with consistent payments.

Q4: Can I use this for extra payments?
A: This assumes regular payments only. For extra payments, you'd need a more complex amortization schedule.

Q5: Why does my balance decrease slowly at first?
A: Early payments are mostly interest due to amortization - the formula accounts for this.