Mortgage Payment Formula
The fixed monthly payment on a conventional mortgage, where P is the loan amount, r is the monthly rate (annual rate ÷ 12 ÷ 100), and n is the number of monthly payments. Extra payments don't change M — they go entirely to principal.
M = P × r(1+r)ⁿ / ((1+r)ⁿ − 1)
Interest Saved by Extra Payments
Each month the schedule charges interest on the remaining balance, so every extra dollar of principal eliminates all the future interest that dollar would have accrued. The calculator rebuilds the full amortization schedule with your extras and reports the difference.
Savings = Normal Total Interest − Total Interest With Extras
How It Works
Enter the loan amount, interest rate, term, and first payment date, and the calculator produces the fixed monthly payment plus a complete 360-month amortization schedule. To model prepayment, add a recurring Extra Monthly Payment (with a start date, so extras can begin partway through the loan) or type one-time Single Extra amounts directly into any month's row of the schedule. Every extra dollar goes straight to principal, so the balance falls faster, later interest charges shrink, and the loan pays off early. The summary compares total payments and total interest with and without your extras.
Example Problem
A $200,000 mortgage at 6.5% for 30 years, first payment January 2026. The borrower adds an extra $200 to every monthly payment. Find the monthly payment, the interest saved, and the new payoff date.
- Compute the monthly rate: r = 6.5 ÷ 12 ÷ 100 = 0.005417.
- Compute the number of payments: n = 30 × 12 = 360.
- Monthly payment: M = $200,000 × r(1+r)ⁿ / ((1+r)ⁿ − 1) = $1,264.14 — extra payments do not change this.
- Each month, pay $1,264.14 + $200; the extra $200 reduces principal directly.
- Rebuild the schedule month by month: interest each month is the remaining balance × 0.005417, so the shrinking balance cuts every later interest charge.
- The balance reaches zero at month 250 instead of 360: total interest falls from $255,088.98 to $165,012.20 — a saving of $90,076.78 and a payoff 9 years 2 months early.
The schedule applies extras exactly where you enter them, so you can combine a recurring extra with occasional one-time payments — the way most people actually prepay.
Key Concepts
Mortgage amortization front-loads interest: early payments are mostly interest because the balance is large. Extra principal payments attack exactly that — a dollar of principal paid in year 1 avoids nearly 30 years of compounding interest on it, while the same dollar in year 25 saves only a few years' worth. That is why identical extra payments save dramatically more when they start earlier, and why even modest recurring extras shorten a 30-year loan by years rather than months.
Applications
- Homeowners testing what an extra $100-500/month does to their payoff date and lifetime interest
- Property managers recording tenant or owner prepayments that arrive irregularly — one-time extras in specific months
- Borrowers with annual windfalls (bonuses, tax refunds) modeling a single extra payment each year
- Budget planning for extras that can only start later — a raise, a paid-off car loan, or a child leaving daycare
- Comparing prepayment against alternatives by putting a hard number on the interest a prepayment strategy saves
- Printing an updated amortization schedule that reflects the payments actually made
Common Mistakes
- Assuming extra payments lower the required monthly payment — they don't; they shorten the loan and cut total interest instead
- Comparing savings against the original balance instead of total interest — the benchmark is the interest column of the normal schedule
- Forgetting to tell the loan servicer that extras are principal-only payments — some servicers apply them to the next payment (including interest) by default
- Ignoring the start date — extras entered with a mid-loan start date leave the earlier months unchanged, which is exactly right for modeling a raise or freed-up budget
- Reading the schedule's PMI-free numbers as the full housing cost — taxes, insurance, escrow, and PMI are not included
Frequently Asked Questions
How do you calculate a mortgage payment with extra payments?
The base payment is M = P × r(1+r)ⁿ / ((1+r)ⁿ − 1), where P is the loan amount, r the monthly rate, and n the number of payments. Extra payments don't change M — each one reduces the principal balance directly, and the amortization schedule is rebuilt month by month with interest charged on the new lower balance. This calculator does that rebuild for recurring extras, one-time extras in any month, or both.
How much does paying an extra $200 a month save on a mortgage?
On a $200,000 mortgage at 6.5% for 30 years, an extra $200/month saves $90,076.78 in interest and pays the loan off 9 years and 2 months early. The exact savings depend on the balance, rate, and when the extras start — enter your own numbers to see your schedule.
Can I enter an extra payment for just one or two months a year?
Yes. Every row of the amortization schedule has a Single Extra column — type an amount into any month's row and the schedule recalculates with that one-time principal payment. Enter one amount per year to model an annual bonus, or several across the loan for irregular prepayments.
Can extra payments start partway through the loan?
Yes. Set the Start of Extra Payments month and year, and the recurring extra applies only from that date forward. Months before the start date follow the normal schedule — useful when a raise or a paid-off debt frees up budget years into the mortgage.
How do I print the amortization schedule?
Click Print Schedule above the table (or use your browser's print command). The printout contains the loan inputs, the payment, the savings summary, and the complete month-by-month schedule including the extra payments you entered.
Does the calculator include PMI, taxes, and insurance?
No. It computes principal and interest only, like the standard amortization formula. Private mortgage insurance, property taxes, escrow, and homeowners insurance vary by lender and location and are not part of the schedule — your actual monthly housing payment will be higher.
Why is the calculator limited to a 30-year term?
The schedule is a fixed 360-row table, matching the most common maximum for conventional fixed-rate mortgages. Any term up to 30 years works — shorter terms simply pay off early and the remaining rows show zero.
Reference:
Amortization formula: Brealey, R., Myers, S., & Allen, F. Principles of Corporate Finance. McGraw-Hill Education.
Mortgage Payment Formula
The fixed monthly payment on a conventional mortgage comes from the standard amortization formula:
Where:
- M — monthly payment, in dollars ($)
- P — loan/mortgage amount, in dollars ($)
- r — monthly interest rate (annual rate ÷ 12 ÷ 100), as a decimal
- n — total number of monthly payments (years × 12)
Extra payments do not change M — they go entirely to principal. Each month the schedule charges interest on the remaining balance (balance × r), so every extra dollar of principal removes all the future interest that dollar would have accrued. That is why the same extra payment saves more the earlier it is made.
Worked Examples
Recurring Extra Payment
What does an extra $200/month save on a $200,000 mortgage?
A homeowner has a $200,000 mortgage at 6.5% for 30 years and adds $200 to every payment starting with the first one.
- Base monthly payment: M = $200,000 × r(1+r)ⁿ / ((1+r)ⁿ − 1) with r = 0.065/12 → $1,264.14.
- Each month, the extra $200 goes entirely to principal.
- The lower balance shrinks every future interest charge.
- The schedule reaches zero at month 250 instead of month 360.
Saves $90,076.78 in interest and pays off 9 years 2 months early
The earlier the extra payments start, the more interest each dollar saves — principal reduced in year 1 avoids 29 years of interest on that amount.
One-Time Extra Payment
How much does a single $5,000 principal payment save?
A borrower with a $150,000 mortgage at 5.75% for 30 years puts a $5,000 tax refund toward principal in month 12.
- Base monthly payment: $875.36 — unchanged by the extra payment.
- Type 5000 into the Single Extra column on row 12 of the schedule.
- The balance drops $5,000 immediately, so every later month accrues less interest.
- The loan pays off at month 332 instead of 360.
Saves $19,707.58 in interest — nearly 4× the $5,000 payment
One-time extras can be entered in any month — model a yearly bonus by typing an amount into one row per year.
Extras Starting Mid-Loan
Is it worth starting extra payments 10 years into a mortgage?
Ten years into a $250,000 mortgage at 6% (first payment January 2026), a borrower's budget frees up $300/month starting January 2036.
- Base monthly payment: $1,498.88.
- Set Start of Extra Payments to January 2036 — months 1-120 stay normal.
- From month 121 on, $300 extra goes to principal each month.
- The schedule reaches zero at month 295 instead of 360.
Saves $45,542.05 in interest and pays off about 5.4 years early
Starting the same $300 extra at month 1 instead would save roughly twice as much — but mid-loan extras still cut deep into the back-loaded interest years.
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