Additional Payment Payoff Calculator: Time and Interest

An additional payment payoff calculator estimates how many months it takes to repay a fixed-rate loan when you pay more than the required monthly amount, and how much interest you pay. Enter the balance, APR, regular payment, and extra monthly amount to see the estimated payoff time and total interest.

Formula

The calculator first combines the regular payment and extra payment, then estimates the number of equal monthly payments needed to bring the balance to zero:

Monthly rate: r = APR / 1200
Payment used in the calculation: m = regular payment + additional payment
Months to payoff: n = ceil(round(−ln(1 − r × balance / m) / ln(1 + r), 6))
Total paid: m × n
Estimated interest: total paid − balance

• Balance is the current principal owed, in dollars.
• APR is the annual percentage rate entered as a percentage, such as 8 for 8% per year.
• r is the monthly rate as a decimal, calculated by dividing APR by 1,200.
• m is the combined monthly payment in dollars.
• n is the estimated number of monthly payments, rounded up to a whole month.

The formula assumes the same combined amount is paid each month. Its logarithm only works for a payment greater than the interest accruing on the balance in one month. If a payment does not cover that interest, the balance will not be paid down under this simplified model.

Worked Example

Using the calculator’s defaults: balance = $20,000, APR = 8%, regular payment = $405.53, and additional payment = $100.

1. Convert the annual rate to a monthly decimal: r = 8 / 1,200 = 0.0066667.
2. Add the payment amounts: m = $405.53 + $100 = $505.53 per month.
3. Substitute into the payoff formula: n = ceil(round(−ln(1 − 0.0066667 × 20,000 / 505.53) / ln(1.0066667), 6)) = 48 months.
4. Estimate total paid: $505.53 × 48 = $24,265.44.
5. Subtract the starting balance: $24,265.44 − $20,000 = $4,265.44 in estimated interest.

Results are rounded to whole months for the payoff estimate and to cents for money. Because the calculator assumes the combined payment continues unchanged throughout the final month, the total paid can be higher than the amount actually required for a smaller final payment.

Assumptions

• The interest rate remains fixed throughout the payoff period.
• Payments are made monthly, with the first payment one month after the starting balance is measured.
• Interest compounds monthly at APR / 12.
• The estimate excludes fees, taxes, insurance, PMI, and escrow, and assumes no new borrowing or payment changes.

When to Use an Additional Payment Calculator

Use this estimate to understand how a recurring extra amount may affect a loan payoff schedule. It can help with comparing hypothetical payment amounts or checking the broad effect of consistently paying above a required amount. The calculation is relevant only when the extra money is applied to the modeled balance. Loan servicing practices can vary, so check how the servicer processes additional payments and whether you need to specify that they should reduce principal.

Enter the current balance, not necessarily the amount originally borrowed. Use the APR and required payment that apply to the loan now. Add only the extra amount you expect to pay each month; a one-time lump-sum payment is not represented by this calculator. If the payment changes, the rate is variable, or payments are made on a different schedule, this result may not closely match the actual timeline.

How to Read the Results

“Months to payoff” is the number of full monthly payment periods implied by the formula. Divide by 12 for a rough years-and-months interpretation; for example, 48 months is four years. “Total paid” multiplies the combined monthly payment by that whole number of months, while “estimated interest” subtracts the starting balance from that total.

These totals are mathematical estimates, not an exact payoff quote. The actual final payment is often smaller than the regular payment because only the remaining principal and accrued interest are due. This calculator does not adjust that final payment, so its total paid and interest can be overstated by part of a payment. It also does not reproduce a lender’s daily interest calculations, payment posting dates, or rounding conventions.

Common Limitations and Misunderstandings

• Extra payment is not a one-time amount: the input represents an additional amount paid every month. A lump sum needs a model that accounts for when it is paid.
• APR is not the monthly rate: enter an annual percentage, such as 8, rather than 0.08 or 0.0067. The calculator converts it to a monthly decimal.
• A payoff estimate is not a lender payoff quote: exact amounts may include interest accrued through a particular date and other account-specific items.
• The model does not include every loan feature: deferred payments, fees added to the balance, changing rates, skipped payments, and payment holidays are not represented.
• Rounding affects the result: the estimate rounds payoff time up to a whole month and applies the same payment for that entire number of months.

If you want to compare an extra payment with a different approach, keep the assumptions consistent and use actual loan terms from the lender. The calculator does not account for other financial priorities or determine whether a payment amount is suitable for an individual.

Frequently Asked Questions

How do I calculate how fast extra payments pay off a loan?
Use the current balance, monthly interest rate, and combined regular-plus-extra payment in a payoff formula. This calculator converts APR to a monthly rate and rounds the estimated number of payments up to a whole month.

Does an extra payment reduce principal?
The calculation assumes additional money reduces the modeled loan balance. Confirm with the servicer how extra amounts are applied; payment allocation can affect the real schedule.

Can I enter a one-time extra payment?
No. The extra-payment field is a recurring monthly amount. A one-time payment needs a calculation that reflects its amount and timing.

Why is my lender’s payoff date different?
The estimate assumes fixed monthly compounding and equal payments. Actual results can differ because of payment dates, daily interest, rate changes, fees, rounding, or a smaller final payment.

What if my payment is too low to cover the interest?
The formula cannot calculate a finite payoff when the monthly payment does not exceed the interest accruing on the balance. A lender can provide the current amount needed to keep the balance from growing.

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

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in bal | Current loan balance | $ | 20000 | 0.01 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in pmt | Regular monthly payment | $ | 405.53 | 0.01 | 100000000
in extra | Additional monthly payment | $ | 100 | 0 | 100000000
out mon | Months to payoff | months | ceil(round(-ln(1 - (apr / 1200) * bal / (pmt + extra)) / ln(1 + apr / 1200), 6)) | 0
out paid | Total paid | $ | (pmt + extra) * mon | 2
out int | Estimated interest | $ | paid - bal | 2