Amortization Calculator With Extra Payments

This amortization calculator shows how an extra monthly payment changes a loan’s payoff schedule and total interest. Enter the loan amount, APR, term, and extra amount; it returns the regular payment, payoff time, total interest, and interest saved compared with making only scheduled payments.

Formula

The scheduled monthly payment uses the standard fixed-payment loan formula:

PMT = round[P × r ÷ (1 − (1 + r)⁻ⁿ), 2]

• P is the starting loan principal in dollars.
• APR is the annual percentage rate entered as a percentage, such as 8 for 8%.
• r is the monthly rate, calculated as APR ÷ 1200.
• n is the scheduled term in months, calculated as years × 12.
• PMT is the regular monthly payment, rounded to cents.

For the estimate with an extra amount, the calculator treats each payment as the scheduled payment plus the extra: M = PMT + extra. It estimates the number of payments as ceil[−ln(1 − rP/M) ÷ ln(1 + r)]. The result is rounded up to a whole month. Total interest is estimated as M × months − P; interest saved is the scheduled-term interest less that estimate. This simplified total assumes the same combined payment every month, including the final month.

Worked Example

Using the default inputs—$20,000 principal, 8% APR, five years, and $100 extra each month:

1. Monthly rate: 8 ÷ 1200 = 0.0066667. Scheduled months: 5 × 12 = 60.
2. Scheduled payment: round[$20,000 × 0.0066667 ÷ (1 − 1.0066667⁻⁶⁰), 2] = $405.53.
3. Combined payment for the estimate: $405.53 + $100 = $505.53.
4. Estimated payoff months: ceil[−ln(1 − 0.0066667 × 20,000 ÷ 505.53) ÷ ln(1.0066667)] = 48 months.
5. Estimated interest with extras: $505.53 × 48 − $20,000 = $4,265.44.
6. Scheduled-payment interest for comparison: $405.53 × 60 − $20,000 = $4,331.80. Estimated interest saved: $4,331.80 − $4,265.44 = $66.36.

The example uses the required rounded scheduled payment in the comparison. The extra-payment estimate assumes the combined amount is paid for every counted month; an actual lender generally adjusts the final payment to the remaining balance, so the displayed interest and savings are approximations rather than a statement payoff quote.

Assumptions

• The interest rate stays fixed throughout the estimate.
• Payments are made monthly, with the extra amount applied alongside each scheduled payment.
• Interest is modelled monthly at APR ÷ 12; actual accrual and posting can differ.
• Fees, taxes, insurance, PMI, escrow, and lender-specific payment allocation are not included.

How Extra Payments Change Amortization

An amortization schedule divides each payment between interest and principal. At the beginning of a typical installment loan, the balance is larger, so more interest accrues for that period. As principal falls, the interest portion generally falls too, leaving more of each later payment to reduce principal.

An extra payment directed to principal reduces the balance sooner. That usually means less interest accrues in subsequent periods and the debt can be repaid earlier. The effect depends on the balance, rate, timing, and amount—not just on the number of extra dollars. A one-time extra payment and a recurring monthly extra payment produce different schedules.

This calculator models a fixed extra amount every month. It does not generate a complete month-by-month ledger or model a one-time lump sum. Its payoff-month output is an estimate based on a repeated combined payment, not a guarantee of the date a lender will mark the loan paid in full.

How to Use and Read the Results

• Enter the current principal balance, rather than the original amount borrowed if payments have already been made.
• Use the APR as a percentage: enter 8 for 8%, not 0.08.
• Enter the remaining scheduled term in years. For a partially paid loan, use the time remaining, not the original term.
• Enter the additional monthly amount separately from the scheduled payment.
• Compare the estimated payoff months and interest with the scheduled-payment baseline shown in the output.

The first output is the regular scheduled payment before the extra amount. The next outputs show estimated months to payoff, estimated interest under the extra-payment assumption, and the difference from scheduled-term interest. A positive savings figure represents lower estimated interest under these assumptions; it is not a statement of a guaranteed saving.

Common Misconceptions and Limits

An extra payment does not always reduce principal automatically. A servicer may apply money according to its payment rules, such as treating it as an advance payment or applying it to another amount due. Check the loan’s statement or ask the servicer how to designate an additional principal payment and whether any charges or restrictions apply. This calculator does not model those terms.

Another common mistake is treating an APR as an exact description of every loan’s interest accrual. The formula here uses a nominal annual rate divided by 12 and monthly periods. A lender may calculate interest using different conventions, and the APR can include cost components that are not represented as monthly interest in this simple formula. The lender’s payment schedule is the appropriate source for exact figures.

Rounding also matters. Scheduled payment is rounded to cents before adding the extra amount, while the estimate assumes that combined amount repeats. Actual payment dates, daily interest, payment posting, changing rates, and a smaller final payment can all make the real payoff total differ. The displayed difference is most useful as a controlled comparison, not an exact accounting result.

Frequently Asked Questions

Does an extra payment go directly to principal?
Not necessarily. Application depends on the loan and servicer’s process. Confirm how to submit or designate extra principal and review the resulting balance.

Does this calculator show a full amortization schedule?
No. It estimates the scheduled payment, payoff months, and interest totals. It does not list each month’s opening balance, interest, principal, and closing balance.

Can I enter a one-time extra payment?
This version is designed for a recurring monthly extra amount. A one-time payment needs a schedule that applies the lump sum in the specific month it is made.

Why might my lender’s payoff date differ?
Actual dates, daily interest, posting rules, variable rates, fees, and a reduced final payment can change the result. Ask the lender or servicer for a current payoff amount and schedule.

What if the extra payment is zero?
The calculator uses the scheduled payment alone as the repeated amount. Its interest comparison is then zero savings, subject to the rounding and simplified assumptions described above.

This result is an estimate for educational purposes, and the lender’s disclosure gives the exact figures.

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in p | Loan amount | $ | 20000 | 1 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in yrs | Loan term | years | 5 | 0.0833 | 50
in extra | Extra payment each month | $ | 100 | 0 | 100000000
out pmt | Scheduled monthly payment | $ | round(p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)), 2) | 2
out time | Months to payoff with extra payment | months | ceil(round(-ln(1 - (apr / 1200) * p / (pmt + extra)) / ln(1 + apr / 1200), 6)) | 0
out tint | Interest with extra payments | $ | (pmt + extra) * time - p | 2
out saved | Interest saved vs scheduled payments | $ | (pmt * yrs * 12 - p) - tint | 2