Loan Amortization Extra Payment Calculator

This loan amortization extra payment calculator estimates how an additional monthly payment changes your payoff time and total interest. Enter the loan balance, APR, remaining term, and extra amount; it returns the revised monthly payment, payoff period, and interest estimate.

Formula

The calculator first finds the scheduled level monthly payment, then estimates how many whole monthly payments are needed when the extra amount is added. The payoff-month calculation assumes the same combined payment is made each month, including the final month; in practice, the last payment is usually smaller. Its interest outputs use that regular-payment approximation.

• Scheduled payment: M = round[P × r / (1 − (1 + r)⁻ⁿ), 2].
• Estimated payoff months: k = ceil[−ln(1 − rP/(M + E)) / ln(1 + r)].
• Estimated interest with extra payments: I_extra = (M + E) × k − P.
• Estimated interest avoided: I_scheduled − I_extra, where I_scheduled = M × n − P.

P is the current loan balance in dollars; APR is the annual percentage rate; r = APR/1200 is the monthly rate as a decimal; n is the remaining term in months; M is the scheduled monthly payment in dollars; E is the extra monthly amount in dollars; and k is the estimated number of payments. Payments are rounded to cents, and payoff time is rounded up to a whole month. The calculation assumes the extra is paid every month, starting with the next payment.

Worked Example

Using the calculator’s defaults: P = $20,000, APR = 8%, term = 5 years, and E = $100 monthly.

1. Convert the term to months: n = 5 × 12 = 60. The monthly rate is r = 8/1200 = 0.0066667.
2. Calculate the scheduled payment: M = round[20,000 × 0.0066667 / (1 − (1.0066667)⁻⁶⁰), 2] = $405.53.
3. Combine the scheduled payment and extra: $405.53 + $100 = $505.53. The payoff formula gives about 44.96 months, rounded up to 45 months.
4. Estimated interest with the extra: $505.53 × 45 − $20,000 = $4,248.85.
5. Scheduled-payment interest estimate: $405.53 × 60 − $20,000 = $4,331.80. Estimated interest avoided: $4,331.80 − $4,248.85 = $82.95.

The interest comparison uses a simplified whole-payment estimate: it treats each of the 45 payments as $505.53, although an actual lender would generally calculate a smaller final payoff amount. Therefore, the displayed interest and savings are estimates rather than a lender payoff quote.

Assumptions

• The interest rate stays fixed for the modeled period.
• Payments are monthly, made at the end of each monthly period, with the first extra payment included in the next payment.
• Interest compounds monthly at APR divided by 12.
• Fees, taxes, insurance, PMI, escrow, late charges, and lender-specific payment allocation are not included.

How an Extra Payment Changes Amortization

An amortizing loan payment covers interest accumulated since the prior payment and reduces principal with what remains. Early in a typical level-payment schedule, the balance is relatively high, so a larger portion of each scheduled payment goes to interest. As principal falls, the interest portion generally declines and more of the payment reduces principal.

An additional amount applied to principal lowers the balance used to calculate future interest. If the scheduled payment continues unchanged, the loan can be paid off earlier and less interest may accrue. The result depends on the balance, rate, timing, and how the servicer applies the money—not merely on the amount labeled “extra.”

How to Use and Read the Estimate

• Enter the current principal balance, not necessarily the original amount borrowed. Use the remaining term, rather than the original term, if payments have already been made.
• Enter the annual APR as a percentage, such as 8 for 8%, and enter the extra amount you expect to pay every month.
• Compare the estimated payoff months and interest avoided with your lender’s amortization schedule. The scheduled payment shown is the formula’s principal-and-interest payment, not necessarily the full amount due on a bill.

For an exact comparison, ask the lender for a current balance and an amortization schedule that reflects the intended payment date and extra-payment handling. A calculator’s estimated interest avoided compares its two modeled schedules; it is not a guaranteed saving or a payoff quote.

Extra Payment Choices and Common Problems

A recurring monthly extra payment is the scenario modeled here. A one-time lump sum, irregular extra payments, or a changing amount requires a month-by-month balance calculation and is not captured by this calculator. In a detailed schedule, each period’s interest is calculated from that period’s opening balance, then the payment is applied and the next balance is found.

Check how the lender handles extra funds. They may need to be designated for principal reduction, and an extra amount may otherwise be treated as an early installment or handled differently under the loan’s terms. Also check whether a prepayment charge or other contractual condition applies; this calculator does not determine those terms. Obtain the lender’s instructions and confirm that the balance was reduced as intended.

Do not confuse reducing the balance with changing the required monthly payment. Paying extra commonly shortens the modeled payoff while the scheduled payment remains the same; it does not necessarily recast or lower the bill. A formal recast or a refinancing calculation is a different scenario with separate terms, possible costs, and an updated payment schedule.

Limits and Comparisons

The formula is for a fixed-rate loan with a monthly schedule and a regular extra amount. It does not model variable rates, daily interest calculations, payment holidays, skipped or late payments, fees added to the balance, or a final payment recalculated to the exact remaining amount. For loans with these features, the lender’s schedule may differ. Small differences can also result from payment-date conventions and rounding each month.

The calculator’s “interest avoided” is a comparison with keeping the same modeled loan and paying only the scheduled amount. It does not account for what else could be done with the extra cash, nor does it establish that extra payments are appropriate for a particular person. It is arithmetic for comparing scenarios, not an overall financial assessment.

Frequently Asked Questions

Does an extra loan payment go toward principal?
It depends on the loan terms and payment instructions. Confirm with the lender how to designate an extra amount and verify how it appears on the account.

Does paying extra lower my required monthly payment?
Not necessarily. This calculator keeps the scheduled payment fixed and estimates an earlier payoff. A lower required payment would generally involve a separate lender process and calculation.

Is the last payment the same size as the regular payment?
Usually, an exact payoff schedule recalculates the final amount to cover the remaining principal and accrued interest. This calculator uses whole monthly payments for its interest estimate, so its implied final payment can be overstated.

Can I enter a one-time extra payment?
No. The extra-payment input represents the same additional amount paid every month. A lump sum needs a schedule that applies it in a particular month and recalculates later interest.

Why does my lender’s payoff amount differ from this estimate?
A payoff quote can include interest through a specific date and may reflect fees, payment timing, rounding, and the lender’s payment-allocation rules. The calculator excludes these details and uses a simplified monthly model.

This result is an estimate for education; the lender’s disclosure and current payoff information provide the exact figures.

Related

• Calculate a Monthly Loan Payment: Formula and Example
• How to Calculate Loan Payments: Formula and Example
• Basic Loan Calculator Payment and Formula

in p | Loan balance | $ | 20000 | 1 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in yrs | Remaining term | years | 5 | 0.0833 | 50
in extra | Extra paid each month | $ | 100 | 0 | 1000000
out pmt | Scheduled monthly payment | $ | round(p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)), 2) | 2
out payoff | Estimated months with extra payment | months | ceil(round(-ln(1 - (apr / 1200) * p / (pmt + extra)) / ln(1 + apr / 1200), 6)) | 0
out int | Estimated interest with extra payment | $ | (pmt + extra) * payoff - p | 2
out save | Estimated interest avoided | $ | pmt * yrs * 12 - p - int | 2