Mortgage Payoff Calculator

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Reviewed by: David Chen, CFA
David is a Chartered Financial Analyst and licensed mortgage advisor with 15 years of experience in residential lending and debt management strategies.

This 4-in-1 Mortgage Payoff calculator helps you explore scenarios for paying off your home loan. Enter any three variables—Loan Amount, Annual Rate, Term, or Monthly Payment—and we will solve for the fourth.

Loan Amount ($) (P)

Annual Rate (%) (R)

Loan Term (Years) (T)

Monthly Payment (P&I) ($) (M)

Mortgage Payoff Formulas

Solve for Monthly Payment (M):
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]

Solve for Loan Amount (P):
P = M [ (1 + i)^n – 1 ] / [ i(1 + i)^n ]

Solve for Loan Term (T):
T = ln(M / (M – Pi)) / (n * ln(1 + i))

Solve for Rate (R):
Solved iteratively (no direct formula)

Formula Source: CFPB – Consumer Finance

Formula Variables

(P) Loan Amount: The original principal balance of your mortgage.
(R) Annual Rate: Your mortgage’s fixed annual interest rate (APR).
(T) Loan Term: The total number of years in your original loan agreement (e.g., 15, 20, or 30).
(M) Monthly Payment: The fixed monthly payment covering only Principal & Interest (P&I). This does *not* include taxes or insurance (escrow).
(i) Monthly Rate: The annual rate divided by 12.
(n) Total Payments: The total number of payments (Term in years * 12).

Related Calculators

What is a Mortgage Payoff Calculator?

A Mortgage Payoff Calculator is a financial tool that helps homeowners understand the relationship between their loan principal, interest rate, term, and monthly payment. While other calculators focus on adding extra payments, this 4-in-1 calculator focuses on the fundamental components of your original loan agreement.

This tool is essential for verifying your loan terms or exploring different scenarios. For example, you can see how much your monthly payment (M) would have been if you had secured a 15-year term (T) instead of a 30-year one. Or, you can input your payment and loan amount to solve for the interest rate (R) you are *really* paying.

By allowing you to solve for any of the four variables, this calculator empowers you to deconstruct your mortgage and understand exactly how it works. This knowledge is crucial when planning for a refinance, considering extra payments, or simply budgeting for your largest monthly expense.

How to Calculate Your Mortgage Payoff Term (Example)

Identify Your Goal
You have a $300,000 mortgage (P) at a 6.5% rate (R). You want to know how long it would take to pay it off if you made a fixed payment of $2,000 per month (M). You want to solve for the Term (T).
Convert Annual Rate to Monthly (i)
First, convert the annual rate to a monthly decimal: i = (6.5% / 100) / 12 = 0.065 / 12 = 0.0054167
Check if Payment Covers Interest
Your monthly interest is P * i = $300,000 * 0.0054167 = $1,625. Since your $2,000 payment is greater than $1,625, the loan can be paid off.
Apply the Loan Term Formula (Solve for n)
Use the formula: n = ln(M / (M – Pi)) / ln(1 + i)
n = ln(2000 / (2000 – 1625)) / ln(1 + 0.0054167)
n = ln(2000 / 375) / ln(1.0054167)
n = ln(5.3333) / 0.005402
n = 1.6739 / 0.005402
n = 309.86 payments
Convert Total Payments to Years (T)
Finally, divide the total payments (n) by 12:
T = 309.86 / 12 = 25.82 Years
By paying $2,000/month (about $104 more than the 30-year payment), you would pay off your mortgage in just under 26 years, saving you over 4 years.

Frequently Asked Questions (FAQ)

Does this calculator include taxes and insurance (escrow)?

No. This calculator is designed to solve for the core relationship between Principal (P), Interest Rate (R), Term (T), and Monthly Payment (M) (which is P&I only). Your total monthly housing payment (PITI) is almost always higher because it includes escrow for property taxes and homeowner’s insurance.

How can I use this to pay off my mortgage faster?

Enter your Loan Amount (P) and Annual Rate (R). Then, enter a shorter Loan Term (T), like 20 years instead of 30. Leave the Monthly Payment (M) blank and hit “Calculate.” The result for (M) will be the new payment you need to make to pay off your mortgage in that shorter timeframe.

Why can’t I solve for the Rate (R) in the example?

There is no simple algebraic formula to solve for the interest rate (R) in an amortizing loan. Our calculator uses a sophisticated iterative “binary search” algorithm. It makes thousands of guesses in a fraction of a second to find the exact rate that makes all the other numbers work together.

What if I have an ARM (Adjustable-Rate Mortgage)?

This calculator is only accurate for fixed-rate mortgages. For an ARM, your interest rate (R) will change after the initial introductory period, which means your monthly payment (M) will also change. You can, however, use this calculator to model your *current* payment at your *current* rate.

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