Loan Payoff Calculator Extra Payment Formula

A loan payoff calculator with extra payments estimates how additional amounts reduce your balance, total interest, and repayment time. Enter the balance, APR, regular payment, and extra payment; the results are estimates based on a fixed rate and the timing assumptions shown below.

Formula

For a fixed-rate loan with monthly payments, the basic payoff-time formula is:

n = ceil[−ln(1 − rB / M) / ln(1 + r)]

• B is the current unpaid principal balance, in dollars.
• APR is the annual percentage rate entered as a percentage, such as 8 for 8%.
• r = APR / 1200 is the monthly interest rate as a decimal.
• M = P + E is the assumed monthly amount applied to the loan: regular payment P plus monthly extra payment E, in dollars.
• n is the estimated number of monthly payments; the calculator rounds up to a whole month.

The formula applies when the payment exceeds the interest charged each month: M > rB. The interest estimate uses M × n − B, assuming the final payment is the same as the regular combined amount. Actual lenders generally adjust the last payment to the remaining balance, so the estimate can differ slightly. The comparison for interest saved uses the same method with the regular payment alone.

Worked Example

Using the calculator’s defaults, the current balance is $20,000, APR is 8%, the regular payment is $405.53, and the monthly extra is $100. The assumed payment toward the loan is $405.53 + $100 = $505.53. The monthly rate is 8 / 1200 = 0.0066667.

1. Insert the figures into the payoff formula: n = ceil[−ln(1 − (0.0066667 × 20,000) / 505.53) / ln(1.0066667)].
2. The expression inside the first logarithm is about 0.7364. The quotient is about 45.45 months, which rounds up to 46 months.
3. Estimated interest with the extra payment is 46 × $505.53 − $20,000 = $3,254.38.
4. With the regular payment alone, the formula gives 58 months. Estimated interest is 58 × $405.53 − $20,000 = $3,520.74. The estimated difference is $266.36.

The rounded month count treats every payment as the same amount, including the final one. A real final payment is often smaller, and payment dates, daily interest, rounding, or fees can change the total. The example is an arithmetic illustration, not a lender quote.

Assumptions

• The APR stays fixed throughout the payoff period.
• Payments are made monthly, with the extra amount applied alongside each regular payment.
• Interest is modelled monthly at APR / 12; this may not match a lender’s daily accrual method.
• The displayed estimate does not include fees, taxes, insurance, PMI, or escrow. It assumes no new borrowing, missed payments, or separate charges added to the balance.

How Extra Payments Change Payoff

Each payment first covers accrued interest under the model; the remainder reduces principal. When an extra amount is paid and applied to principal, the next period’s interest is calculated on a lower balance. Repeating that process can reduce both the time outstanding and the total interest. The effect depends on the balance, rate, payment schedule, and when the lender applies the additional money.

The calculator assumes an extra payment is made every month. A one-time lump sum is a different schedule: it reduces the balance once, after which the ordinary payment continues. For that situation, calculate the balance after the lump sum is applied and use the new balance as the starting amount, while accounting for the actual date and any interest accrued first.

“Extra payment” should mean money that goes to principal, not merely an advance payment for a future due date. How a servicer handles an additional amount varies by loan and its payment instructions. Check the loan statement or ask the servicer how to designate it; the calculator cannot determine the lender’s processing method.

Using the Results and Checking the Inputs

Use the current principal balance rather than the original amount borrowed. The regular payment should be the amount that actually services principal and interest, not a combined bill that includes escrow or insurance. If the payment includes non-loan items, using the full bill will overstate how much reduces the loan.

• Find the unpaid balance and APR on a current statement or lender disclosure.
• Enter the monthly principal-and-interest payment, then enter only the recurring additional amount you intend to model.
• Read months to payoff as an approximate count of monthly periods, not a guaranteed calendar date.
• Compare estimated interest with extra payments against the regular-payment estimate. The difference is a modelled amount, not a promised saving.

The payment input must exceed monthly interest for the formula to produce a finite payoff estimate. For example, at a $20,000 balance and 8% APR, estimated monthly interest at the start is about $133.33. A combined payment at or below that amount would not reduce principal under this simplified model. The formula’s logarithm also becomes invalid in that case, so a calculator should reject or flag it rather than show a misleading payoff period.

Common Formula Limits

Actual loan calculations may use daily interest, payment dates, variable rates, irregular extra payments, or a different final payment. A variable rate can change the future interest charge, so a fixed-rate projection cannot represent it reliably. Late charges, payment allocation rules, prepayment terms, and fees are also outside this arithmetic unless separately modelled.

Rounding matters. The regular payment shown on a statement may already be rounded to cents, while the lender’s balance and interest calculations may carry more precision internally. This calculator uses the entered payment as given and rounds the payoff period up to a whole month. Consequently, its interest comparison may not match a lender’s payoff quote to the cent.

Do not confuse APR with a monthly rate: 8% APR is entered as 8, then divided by 1200 to obtain the monthly decimal rate. Entering 0.08 as the APR would instead mean 0.08% under this input convention. For an exact payoff amount on a specific date, use the lender’s current figures, since accrued interest and payment posting dates affect the amount due.

Frequently Asked Questions

What is the formula for paying off a loan early with extra payments?
For a fixed monthly rate r, balance B, and total monthly payment M, estimate months as ceil[−ln(1 − rB/M) / ln(1 + r)]. Here M is the regular payment plus the recurring extra amount.

Does an extra payment go straight to principal?
Not necessarily. Payment handling depends on the loan and servicer. Confirm that additional money will be applied to principal rather than held for a future scheduled payment.

Can I use this formula for a one-time extra payment?
The calculator models a recurring monthly extra. For a lump sum, first determine the balance after it is applied, then recalculate using that balance and the payment schedule that follows.

Why does my lender’s payoff estimate differ?
Lenders may calculate interest daily, use a different payment posting date, adjust the last payment, or include accrued interest and charges. This calculator uses simplified monthly compounding and fixed payments.

What if my payment is less than the monthly interest?
The balance will not decline under the model, so there is no finite payoff time from that payment. Check the balance, APR, payment amount, and whether the payment includes principal-and-interest only.

This result is an estimate; 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 | Extra payment per month | $ | 100 | 0 | 100000000
out months | Months to payoff with extra | months | ceil(round(-ln(1 - (apr / 1200) * bal / (pmt + extra)) / ln(1 + apr / 1200), 6)) | 0
out int | Estimated interest with extra | $ | (pmt + extra) * months - bal | 2
out base | Months at regular payment | months | ceil(round(-ln(1 - (apr / 1200) * bal / pmt) / ln(1 + apr / 1200), 6)) | 0
out save | Interest saved vs regular payment | $ | (pmt * base - bal) - int | 2