What does the mortgage payoff calculator do?

It estimates how extra payments—monthly or one-time—shorten your payoff time and reduce total interest on a fixed-rate mortgage.

Does making one extra payment per year help?

Yes. Even an annual lump sum applied to principal can shave months off your term and save interest, especially early in the loan.

Are results exact to the cent?

They are high-precision estimates. Actual lender amortization may differ slightly due to rounding, payment dates, escrow, or fees.

Can I input a 0% interest rate?

Yes. The calculator switches to a zero-interest formula where monthly payment equals principal divided by remaining months.

Will prepayment penalties affect the result?

Potential prepayment penalties are not included. Check your note and lender; penalties can reduce or offset savings.

No. This tool models principal and interest only. Taxes, insurance, and PMI are excluded for clarity.

Mortgage Payoff Calculator | Extra Payments, Time Saved & Interest Savings

Data Source and Methodology

Primary Source: OpenStax, “Business Mathematics,” Section 13.5: Amortized Loans (2018). https://openstax.org/details/books/business-mathematics

Government Guidance: Consumer Financial Protection Bureau (CFPB), “What is amortization and how does it work?” (2020-11-20). https://www.consumerfinance.gov/ask-cfpb/what-is-amortization-en-1065/

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da queste fonti autorevoli.

The Formula Explained

Monthly rate: $ i = \text{APR}/100/12 $
Standard payment (given balance $B$ and $n$ months):
$ M = B \cdot \big[ i / \big(1 - (1 + i)^{-n}\big) \big] $ for $ i > 0 $; otherwise $ M = B/n $.

New payoff months when adding monthly extra $E$ (no lump sum):
$ n' = \left\lceil - \dfrac{\ln\!\big(1 - i\,B/(M+E)\big)}{\ln(1+i)} \right\rceil $.

Amortization update each month (simulation used for lump sums):
$ \text{Interest}_t = B_t \cdot i $; $ \text{Principal}_t = \text{Payment}_t - \text{Interest}_t $; $ B_{t+1} = \max(0, B_t - \text{Principal}_t) $.

Glossary of Variables

B (Balance): Current principal owed on the loan.
APR: Annual percentage rate (nominal), used to derive the monthly rate.
i: Monthly interest rate (APR/12).
n: Remaining number of months on the mortgage.
M: Scheduled monthly principal-and-interest payment with no extra.
E: Extra amount added to each monthly payment (if selected).
n' New number of months to payoff when making extra payments.
L: One-time lump sum applied to principal at a chosen future month.

How It Works: A Step-by-Step Example

Suppose your current balance $ B = \$300{,}000 $ at APR $ = 6\% $ with 25 years remaining ($ n = 300 $ months). The monthly rate is $ i = 0.06/12 = 0.005 $.

$ M = 300000 \times \big[ 0.005 \,/\, (1 - (1.005)^{-300}) \big] \approx \$1{,}933.28 $

Now add a monthly extra $ E = \$200 $, so the total payment is $ M + E \approx \$2{,}133.28 $. Using the payoff formula:

$ n' = \left\lceil - \dfrac{\ln\!\big(1 - 0.005 \times 300000 / 2133.28\big)}{\ln(1.005)} \right\rceil \approx 255 \text{ months} $

You would be debt-free about 45 months sooner (≈ 3 years and 9 months earlier), saving tens of thousands in interest. If you choose a single lump sum early in the schedule, the calculator simulates amortization month-by-month to show the impact precisely.

Frequently Asked Questions (FAQ)

Does the calculator include taxes, insurance, or PMI?

No. It models principal and interest only so you can isolate the effect of extra payments.

What if my APR changes?

This tool assumes a fixed APR. For adjustable-rate mortgages, results will differ when the rate resets.

Is biweekly payment support available?

Not directly, but you can approximate by entering a monthly extra equal to half a payment every month.

Why are my lender’s numbers slightly different?

Lenders may apply daily interest, vary posting dates, and round to the cent each cycle. Those operational details can create small differences.

Can I model multiple lump sums?

This version supports one lump sum. You can approximate multiple by running separate scenarios or using the monthly extra field.

What if my scheduled payment is too low to amortize?

If payment ≤ monthly interest, the balance won’t decrease. Increase the extra payment or verify your remaining term and APR.

Tool developed by Ugo Candido. Content verified by the CalcDomain Editorial Team.
Last reviewed for accuracy on: September 13, 2025.

Mortgage Payoff Calculator

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