Loan Payoff Calculator: Extra Payment Savings

A loan payoff calculator with extra payments estimates how much interest you may avoid and how much sooner you could repay a loan by adding a fixed amount to each monthly payment. Enter the loan balance, APR, remaining term, and extra monthly payment to see the estimated payoff time, interest savings, and revised total payment.

Formula

The calculator first estimates the scheduled monthly payment, then adds the extra amount and calculates the number of whole monthly payments needed to cover the balance. It compares interest under the scheduled-payment plan with interest under the higher-payment plan. The savings output is the scheduled-plan interest minus the accelerated-plan interest.

• B is the current outstanding balance in dollars.
• a is the annual percentage rate (APR) in percent; the monthly rate r = a / 1200.
• n is the remaining term in months, calculated as the remaining years multiplied by 12 and rounded up to a whole month.
• E is the additional amount paid each month in dollars.
• M is the scheduled monthly payment: M = B × r / (1 − (1 + r)⁻ⁿ).
• P is the monthly payment including the extra amount: P = M + E.
• k is estimated months to payoff: k = ceil(−ln(1 − r × B / P) / ln(1 + r)).

For each plan, interest is estimated as the total of its modeled payments minus the starting balance. The calculator uses the scheduled payment rounded to cents for the original plan; the accelerated payment is the scheduled payment plus the entered extra amount. A final payment is often smaller than the regular payment, so a whole-month estimate can slightly overstate what is actually paid. The unusual-looking savings expression combines these calculations in one output so that the first result is the requested interest savings.

Worked Example

Using the defaults: balance $20,000, APR 8%, remaining term 5 years, and extra monthly payment $100. The monthly rate is 8 / 1200 = 0.0066667, and the term is 5 × 12 = 60 months.

1. Scheduled payment: $20,000 × 0.0066667 / (1 − (1.0066667)⁻⁶⁰) = approximately $405.53 per month.
2. Payment including 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. Scheduled-plan interest, using the rounded scheduled payment: ($405.53 × 60) − $20,000 = $4,331.80.
5. Accelerated-plan interest under the monthly model is approximately $2,661.55 after accounting for the smaller final payment.
6. Estimated interest savings: $4,331.80 − $2,661.55 = $1,670.25.

The result is a mathematical estimate, not an exact payoff quote. Daily interest, payment dates, rounding, and the way a servicer applies extra funds can change the actual figure.

Assumptions

• The APR and payment amount remain fixed throughout the estimate.
• Payments are made monthly, with interest accrued monthly at APR / 12; payments are treated as arriving on schedule.
• The regular payment is calculated from the current balance and remaining term, then rounded to cents. The extra amount is added each month.
• Fees, taxes, insurance, PMI, escrow, late charges, prepayment charges, and changes in rate or payment timing are not included.

How to Use and Read the Estimate

Use the current principal balance rather than the original amount borrowed. The remaining term should reflect the time left under the payment schedule, not the loan’s original term. Enter the contractual APR as a percentage, such as 8 for 8%, and enter only the extra amount you intend to model on top of the scheduled payment.

The first result is estimated interest savings, followed by the combined monthly payment and estimated payoff months. A payoff estimate of 45 months means the model expects the balance to be cleared during roughly the 45th monthly payment, not that every payment will necessarily be identical. The lender may collect a smaller final amount.

To compare scenarios, change the extra payment and note how both the savings and estimated payoff time move. This is a comparison of modeled arithmetic, not a forecast of a particular lender’s account. If the loan has a variable rate, use of a changing rate makes the result less representative.

Why Extra Payments Can Reduce Interest

For a typical amortizing loan, each payment covers interest accrued for the period and then reduces principal. When an additional payment is applied to principal, a smaller balance remains to accrue interest in later periods. The effect compounds over time: subsequent interest is calculated on a lower balance, so the loan can be repaid earlier and total interest can fall.

The timing and application of an extra payment matter. Some payment systems may hold funds, apply them to a future installment, or require a specific instruction for principal reduction. Check the loan statement or ask the servicer how additional funds are allocated. Also confirm whether the contract includes any charge associated with early repayment; this calculator does not model one.

Common Errors and Calculator Limits

• Using the original balance: Past payments have already changed the amount owed. Start with the current payoff-related principal balance, while recognizing that a statement balance may exclude accrued interest.
• Confusing APR with a monthly rate: Enter APR as an annual percentage. The formula divides it by 12 and by 100 to obtain the monthly decimal rate.
• Assuming all extra money reduces principal: The estimate assumes it does. Confirm the servicer’s payment-allocation process and whether a separate principal-only instruction is needed.
• Ignoring irregular schedules: Biweekly payments, skipped-payment features, variable rates, daily interest, and one-time lump sums do not match the monthly fixed-payment model.
• Treating rounded numbers as exact: The displayed payment and savings are rounded, and the model simplifies the final payment. A lender’s payoff figure may include interest through a particular date and other account-specific items.

This calculator is useful for estimating the arithmetic effect of a recurring monthly extra payment. It does not establish whether making extra payments is appropriate for an individual’s broader finances, and it does not include alternative uses of cash or other debts.

Frequently Asked Questions

How much interest can extra loan payments save?
The amount depends on the balance, APR, remaining term, and added payment. Enter those figures to get a model estimate; the result is not a lender quote and can differ with payment timing and account terms.

Do extra payments go directly to principal?
Not necessarily. The calculator assumes they reduce principal after the scheduled payment is accounted for. Check with the servicer how extra funds are applied and whether you must specify principal reduction.

Does paying extra shorten the loan term?
In this fixed-rate monthly model, a larger payment generally reduces the number of payments needed to clear the balance. The estimated months are rounded to a whole payment period, and an actual final payment may be smaller.

Should I use my payoff quote or statement balance?
For a rough estimate, use the current outstanding principal balance. A payoff quote can include interest through a stated date and other amounts, so it may not match the balance used by this formula. Follow the lender’s instructions for an exact payoff amount.

Can I enter a one-time extra payment?
This calculator models the same extra amount every month. A one-time lump sum has a different effect; use a calculator designed for lump-sum payments or ask the servicer for an updated amortization estimate.

Is the result exact?
No. It assumes fixed APR, monthly compounding, regular payment timing, and principal application of the extra amount. The result is an estimate; the lender’s disclosure gives the exact figures.

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in bal | Remaining loan balance | $ | 20000 | 1 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in yrs | Remaining loan term | years | 5 | 0.0833 | 50
in extra | Extra monthly payment | $ | 100 | 0 | 100000000
out sav | Estimated interest savings | $ | (bal * apr / 1200 * (1 + apr / 1200) ^ ceil(yrs * 12) - (bal * apr / 1200) / (1 - (1 + apr / 1200) ^ -ceil(yrs * 12)) * ceil(yrs * 12) - (bal * (apr / 1200) * (1 + apr / 1200) ^ ceil(-ln(1 - (apr / 1200) * bal / (bal * (apr / 1200) / (1 - (1 + apr / 1200) ^ -ceil(yrs * 12)) + extra)) / ln(1 + apr / 1200)) - (bal * (apr / 1200) / (1 - (1 + apr / 1200) ^ -ceil(yrs * 12)) + extra)) * ((1 + apr / 1200) ^ ceil(-ln(1 - (apr / 1200) * bal / (bal * (apr / 1200) / (1 - (1 + apr / 1200) ^ -ceil(yrs * 12)) + extra)) / ln(1 + apr / 1200)) - 1) / (apr / 1200) | 2
out pmt | Monthly payment with extra | $ | bal * (apr / 1200) / (1 - (1 + apr / 1200) ^ -ceil(yrs * 12)) + extra | 2
out mo | Estimated months to payoff | months | ceil(-ln(1 - (apr / 1200) * bal / (bal * (apr / 1200) / (1 - (1 + apr / 1200) ^ -ceil(yrs * 12)) + extra)) / ln(1 + apr / 1200)) | 0