Loan Repayment With Extra Payment Calculator

This loan repayment with extra payment calculator estimates how a recurring extra amount changes your monthly payment, total interest, and payoff time on a fixed-rate loan. Enter the balance, annual percentage rate (APR), remaining term, and extra amount; the results compare the scheduled loan with a payment that includes the extra amount.

Formula

The calculator first finds the regular level monthly payment, rounded to cents, then adds the recurring extra amount. It estimates the number of months to repay using that combined payment and calculates interest as total payments less the starting balance.

• p is the current loan balance in dollars.
• apr is the annual percentage rate in percent; the monthly rate is r = apr / 1200.
• n is the remaining scheduled term in months, calculated as years × 12.
• pmt is the regular monthly payment: round(p × r / (1 − (1 + r)⁻ⁿ), 2).
• extra is the additional amount paid each month, in dollars; newpmt = pmt + extra.
• k is the estimated payoff month: ceil(round(−ln(1 − r × p / newpmt) / ln(1 + r), 6)).
• Interest with extra is estimated as newpmt × k − p. Estimated interest saved is the scheduled-term interest, pmt × n − p, less interest with extra payments.

This is a comparison of two simplified payment paths. Actual final payments are often smaller than the regular monthly amount because the remaining balance is less than a full payment by the payoff date. The estimate uses the combined payment for every payoff month, so it does not separately adjust the final payment.

Worked Example

Using the calculator’s default inputs: balance $20,000, APR 8%, remaining term 5 years, and extra monthly payment $100:

1. Convert the rate: r = 8 / 1200 = 0.0066667 per month. The term is 5 × 12 = 60 months.
2. Calculate the scheduled payment: round(20,000 × 0.0066667 / (1 − (1.0066667)⁻⁶⁰), 2) = $405.53.
3. Add the extra amount: $405.53 + $100 = $505.53 per month.
4. Estimate payoff time: ceil(round(−ln(1 − 0.0066667 × 20,000 / 505.53) / ln(1.0066667), 6)) = 46 months.
5. Estimate interest with extras: $505.53 × 46 − $20,000 = $3,254.38.
6. Scheduled-term interest is $405.53 × 60 − $20,000 = $4,331.80; estimated interest saved is $4,331.80 − $3,254.38 = $1,077.42.

The calculator outputs are therefore a $405.53 scheduled payment, $505.53 combined monthly payment, $3,254.38 estimated interest with extras, and $1,077.42 estimated interest saved. The calculation applies its rounded payment at each estimated payoff month; a lender’s exact payoff amount can differ.

Assumptions

• The interest rate stays fixed throughout the modeled repayment period.
• Payments occur monthly, with interest accruing at the monthly rate APR / 12.
• The extra payment is made every month in addition to the scheduled payment and is applied to the loan balance.
• The calculation does not include fees, taxes, insurance, PMI, escrow, variable-rate changes, or lender-specific payment allocation rules.

When to Use the Calculator

Use it to estimate the arithmetic effect of adding a consistent monthly amount to a fixed-rate loan payment. It can help answer two practical questions: how quickly could the modeled balance be repaid, and how does estimated interest compare with making only the scheduled payment?

Enter the current principal balance, not necessarily the original amount borrowed. For a loan already in repayment, use the remaining term and the APR that applies now. The regular payment shown is calculated from those inputs, so it may not match a bill if the loan has fees, a different payment schedule, or a payment that includes other charges. Use the lender’s current statement and disclosure for the actual figures.

How to Read the Results

Scheduled monthly payment is the formula’s level payment for the balance and term entered. Monthly payment with extra is that payment plus the extra amount. The interest estimate is based on paying the combined amount until the calculated payoff month. Estimated interest saved compares that estimate against the scheduled payment over the original remaining term.

These results are estimates, not a revised loan schedule or payoff quote. The calculator assumes the entire extra amount reduces the balance. Some loan arrangements may handle extra funds differently, such as applying them to a future payment rather than principal unless the borrower gives a specific instruction. Check the loan documents or ask the servicer how additional payments are credited. Do not treat the displayed interest difference as a guaranteed saving.

Common Errors and Limits

• Using the original balance: For an existing loan, enter the current unpaid balance. An earlier balance can overstate payoff time and interest.
• Entering APR as a decimal: Enter 8 for 8%, not 0.08. The formula converts the annual percent to a monthly rate.
• Mixing payment intervals: This model expects a monthly extra amount. A one-time lump sum or irregular extras require a schedule that represents when each payment is made.
• Assuming a lower bill: Extra principal payments generally change the modeled payoff path, not the contract’s required scheduled payment. The regular amount may still be due each month.
• Ignoring rounding and timing: The regular payment is rounded to cents and payoff time is rounded up to a whole month. Daily interest, payment dates, and the final partial payment can alter actual totals.

The formula requires a positive APR and a combined payment large enough to cover the month’s interest. If the payment does not cover interest, the loan will not amortize under this model. It also assumes a fixed rate and equal monthly payments; it does not model a variable rate, skipped payments, late charges, changing extras, or a different compounding convention.

Frequently Asked Questions

Does an extra payment reduce the monthly payment?
No. This calculator adds the extra amount to the scheduled payment. It estimates earlier repayment; it does not recast the loan or change the required contractual payment.

Should an extra payment be marked for principal?
The calculation assumes the extra amount is applied to the balance. How to designate an additional payment depends on the servicer’s process and loan terms, so check those details before relying on this estimate.

Can I enter a one-time extra payment?
No. The extra-payment input represents the same additional amount paid every month. A one-time payment needs a calculator or amortization schedule that records its amount and date separately.

Why does the lender’s payoff date differ?
Actual interest may accrue daily, payment dates may vary, and the final payment is typically adjusted to the precise remaining amount. The lender may also use different payment-crediting or rounding rules.

Does the estimate include fees or escrow?
No. It models principal and interest only. Fees, taxes, insurance, PMI, and escrow are not included, and the actual loan disclosure or servicer statement provides the applicable amounts.

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

Related

• Loan Extra Pay Calculator: See Interest and Time Saved
• JPMorgan Loan Payment Calculator and Formula
• Loan Amortization Extra Payment Calculator

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 payment each month | $ | 100 | 0 | 100000000
out pmt | Scheduled monthly payment | $ | round(p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)), 2) | 2
out newpmt | Monthly payment with extra | $ | pmt + extra | 2
out int | Interest with extra payments | $ | newpmt * ceil(round(-ln(1 - (apr / 1200) * p / newpmt) / ln(1 + apr / 1200), 6)) - p | 2
out saved | Estimated interest saved | $ | (pmt * yrs * 12 - p) - int | 2