Repayment Calculator With Extra Payments

This repayment calculator with extra payments estimates your monthly payment, total interest, and payoff time when you add a fixed amount to each scheduled payment. Enter the loan amount, APR, term, and extra monthly payment; the estimates show how the added amount changes repayment under a fixed-rate model.

Formula

The calculator first finds the scheduled monthly payment, then adds the extra amount to estimate the monthly cash payment. It estimates payoff months using the standard amortization equation for a fixed monthly payment, treating the extra as additional principal under the model.

• Scheduled payment: M = round[P × r / (1 − (1 + r)⁻ⁿ), 2].
• Monthly payment including extra: M_x = M + E.
• Estimated months to repay: k = ceil[−ln(1 − rP / M_x) / ln(1 + r)].
• Estimated interest with extra: I_x = max(0, (M_x − E) × k − P). Since M_x − E is the scheduled payment, this expression approximates total paid toward the loan before subtracting principal.
• Interest reduction: scheduled-term interest minus estimated interest with extra, not below zero.

P is the starting principal in dollars; APR is the annual percentage rate in percent; r = APR / 1200 is the monthly rate as a decimal; n is the original term in months; E is the extra monthly amount in dollars; M is the scheduled monthly payment; and k is the estimated number of monthly payments. The extra is assumed to be made in addition to the scheduled payment and credited to the balance. The formula uses rounded scheduled payments and a whole-number payoff month count, so the final payment may in reality be smaller.

Worked Example

Using the defaults—P = $20,000, APR = 8%, term = 5 years, and E = $100—the monthly rate is 0.08 / 12 = 0.0066667, and the term is 5 × 12 = 60 months.

1. Scheduled payment: $20,000 × 0.0066667 / [1 − (1.0066667)⁻⁶⁰] = $405.53 after rounding.
2. Payment with the extra: $405.53 + $100 = $505.53 per month.
3. Estimated payoff time: ceil[−ln(1 − 0.0066667 × $20,000 / $505.53) / ln(1.0066667)] = 45 months.
4. Estimated interest with extra: ($505.53 − $100) × 45 − $20,000 = $249.00.
5. Scheduled-payment interest under the same rounded-payment model: $405.53 × 60 − $20,000 = $4,331.80. Estimated interest reduction: $4,331.80 − $249.00 = $4,082.80.

This simplified estimate counts a full scheduled payment in each payoff month, so it does not calculate the smaller final payment or its precise interest. The result is therefore an illustration, not a lender payoff quote.

Assumptions

• The interest rate remains fixed for the modeled repayment period.
• Payments occur monthly at the end of each period, with the first payment one month after borrowing.
• Interest compounds monthly at APR / 12.
• The extra payment is made every month, in addition to the scheduled payment, and is applied to principal.
• Fees, taxes, insurance, PMI, escrow, late charges, and lender-specific payment allocation are not included.

How Extra Payments Change Repayment

Loan payments typically cover accrued interest first, with the remainder reducing principal. When the balance falls sooner, later interest is calculated on a smaller amount. An extra payment can therefore reduce both the time in debt and the interest accumulated, assuming the servicer applies it as principal rather than advancing the next due date.

The calculator’s extra-payment input is a fixed amount added each month. It does not model a one-time lump sum, a changing extra amount, skipped payments, or an extra payment made on a particular date. Timing matters: an additional amount applied earlier can have a different effect from the same amount applied later.

How to Use and Read the Results

• Enter the current principal balance rather than the original amount borrowed if payments have already been made.
• Enter the APR as a percentage, such as 8 for eight percent—not 0.08.
• Enter the remaining term in years, and the extra amount you expect to pay each month.
• Compare the payment, interest estimate, and interest-reduction estimate with the scheduled-payment baseline.

The “Monthly payment with extra” result is the scheduled payment plus the extra amount, not a revised contractual minimum. The savings figure is an estimate against making only the scheduled payment for the full term. Actual savings and payoff timing depend on balance, payment dates, rounding, variable-rate changes, and how the lender handles additional funds. Use the loan statement or servicing information for the actual balance and payment instructions.

Common Issues and Limits

A common misconception is that any amount paid above the bill automatically reduces principal immediately. Payment handling varies, so check the lender’s instructions for directing extra funds to principal and whether a separate designation is needed. The calculator assumes the extra is applied that way.

Another limitation is the final payment. The formula rounds the scheduled payment to cents and estimates a whole number of months; a real loan usually has a final amount adjusted to clear the remaining balance. The interest estimate here uses a simplified whole-payment calculation and may differ from an amortization schedule that calculates each month’s declining balance and exact final payment.

Results can also differ if the rate changes, interest accrues daily, payments are irregular, or fees are added to the balance. For a more detailed comparison, use the lender’s current principal, payment schedule, rate terms, and specific rules for extra payments. A calculator cannot establish whether a particular payment plan suits an individual’s circumstances.

Frequently Asked Questions

Does an extra payment go directly to principal?
Not necessarily. This estimate assumes the lender applies the extra amount to principal. Check the payment instructions or contact the servicer to confirm how additional funds are allocated.

Can I enter a one-time extra payment?
This calculator models the same extra amount every month. A one-time lump sum needs a different calculation that accounts for its date and the balance at that point.

Why is the calculator’s payoff estimate different from my lender’s?
Differences can come from payment dates, daily interest, rounding, variable rates, fees, the exact outstanding balance, or how extra funds are applied. The estimate also approximates the final payment.

Does a larger monthly payment always reduce total interest?
In this fixed-rate model, a larger payment applied to principal shortens repayment and reduces modeled interest. Real results depend on the loan terms and payment allocation.

Should I use APR or the interest rate?
Use the APR requested by this calculator as a model input, but verify which rate the loan’s repayment schedule uses. Fees and APR conventions may not be represented by this simple monthly-interest formula.

This result is an estimate, 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 per month | $ | 100 | 0 | 100000000
out pmt | Monthly payment with extra | $ | round(p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)), 2) + extra | 2
out int | Estimated interest with extra | $ | max(0, (pmt - extra) * ceil(round(-ln(1 - (apr / 1200) * p / (pmt - extra)) / ln(1 + apr / 1200), 6)) - p) | 2
out save | Interest reduction vs scheduled payments | $ | max(0, (round(p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)), 2) * yrs * 12 - p) - int) | 2