Loan Extra Repayment Calculator: Estimate Interest Savings

This loan extra repayment calculator estimates how adding a fixed amount to each monthly payment changes your payoff time and total interest. Enter the loan balance, annual percentage rate, remaining term, and extra monthly amount to see an estimated new payoff period and interest savings.

Formula

The calculator first estimates the scheduled monthly payment for a fixed-rate loan using the standard amortizing-loan payment formula, rounded to cents:

PMT = round(P × r / (1 − (1 + r)^−N), 2)

Here, P is the starting balance in dollars, r = APR / 1200 is the monthly rate as a decimal, and N = years × 12 is the number of monthly payments. It then treats the extra amount as part of each monthly payment, so the modeled payment is M = PMT + extra. The estimated number of payments is ceil(round(−ln(1 − rP/M) / ln(1 + r), 6)).

Estimated interest without extra repayments is scheduled payment times scheduled months minus principal. Estimated interest with extra repayments is modeled payment times estimated months minus principal. Interest saved is the difference between those two estimates. Money outputs are rounded to cents; the payoff period is rounded up to a whole month.

Worked Example

Using the defaults—$20,000 balance, 8% APR, five years remaining, and $100 extra per month:

• Monthly rate: 0.08 / 12 = 0.0066667.
• Scheduled months: 5 × 12 = 60.
• Scheduled payment: round(20000 × 0.0066667 / (1 − (1.0066667)^−60), 2) = $405.53.
• Modeled payment with the extra: $405.53 + $100 = $505.53.
• Estimated payoff time: ceil(round(−ln(1 − 0.0066667 × 20000 / 505.53) / ln(1.0066667), 6)) = 46 months.
• Scheduled interest estimate: $405.53 × 60 − $20,000 = $4,331.80.
• Interest estimate with extra payments: $505.53 × 46 − $20,000 = $3,254.38.
• Estimated interest saved: $4,331.80 − $3,254.38 = $1,077.42.

The calculator’s savings result uses the same rounded payment and whole-month payoff convention shown here. Actual final payments are often smaller than a regular payment when the remaining balance is less than the scheduled amount.

Assumptions

• The interest rate remains fixed throughout the modeled payoff.
• Payments are made monthly, with the extra amount added to each scheduled payment.
• Interest is modeled monthly at APR divided by 12.
• Fees, taxes, insurance, PMI, escrow, and lender-specific payment allocation are not included.

What Extra Repayment Changes

A regular loan payment covers interest accrued for the period and reduces the amount borrowed. When an additional payment is applied to principal, the balance falls faster. Later interest is then calculated on a smaller balance, which can reduce the total interest paid and shorten the repayment period. The precise outcome depends on the loan’s terms and how the lender processes extra amounts.

“Extra repayment” can mean a one-time lump sum, a recurring monthly addition, or paying more frequently. This calculator models one specific case: the same extra dollar amount is added every month. It does not model a lump sum, skipped payments, variable payment amounts, or a changing rate.

How to Use and Interpret the Estimate

Use the current principal balance and the rate and remaining term that apply to that balance—not the original amount and original term if payments have already been made. Enter the extra amount you expect to pay each month. If no extra payment is planned, enter zero.

The interest-saved figure is a comparison between two mathematical estimates, not a guaranteed amount. It assumes the scheduled payment is the standard amortizing payment calculated from the balance, APR, and term provided. If the actual required payment differs because of fees, payment timing, or a lender’s calculation method, the comparison may not match the account statement.

The payoff-month result is rounded up because the model counts complete monthly payment periods. It uses the full modeled payment for each counted month, including the last one. A real lender may instead calculate a smaller final payoff amount, and daily interest or payment dates can alter the exact figure.

Common Issues and Limits

• Extra money may not reduce principal automatically. Check the lender’s instructions for applying additional payments. Depending on the account terms, an amount might be treated as an advance payment rather than a principal reduction.
• Prepayment charges or restrictions may apply. The calculator does not know a loan’s contract. Review the loan documents or ask the lender whether additional payments have conditions or charges.
• APR is a model input, not always the exact interest calculation rate. APR can reflect costs beyond the note rate, while this formula uses APR as the monthly interest rate. For a precise estimate, use the rate and method specified for the loan balance by the lender.
• Rounding and timing matter. The scheduled payment is rounded to cents, while lenders may accrue interest daily and post payments on particular dates. Even small differences accumulate.
• Variable rates are not represented. The estimate assumes one unchanged rate for the entire remaining term.

This is educational arithmetic, not financial advice. The right figures to enter are the ones shown in the loan disclosure or confirmed by the lender; this calculator does not determine whether an extra payment fits any individual circumstances.

Frequently Asked Questions

Does making extra loan payments reduce interest?
It can reduce interest when the extra amount is applied to principal, because a lower balance generally results in less interest accruing afterward. The account’s terms and payment handling determine the actual effect.

Should I tell the lender to apply extra money to principal?
Ask the lender how to designate an additional payment and confirm how it was posted. The calculator assumes every extra monthly amount reduces principal rather than being held or applied to a future scheduled payment.

Can I use this calculator for a one-time lump-sum payment?
No. It models a recurring fixed extra amount every month. A lump-sum payment requires a separate calculation that accounts for when the payment is made and the balance at that date.

Why does the calculator show a different payoff date than my lender?
Possible causes include daily interest, payment posting dates, a different balance or rate, fees, a variable rate, and whether extra payments were applied to principal. Request an updated payoff estimate from the lender for an account-specific figure.

Does an extra payment change my required monthly payment?
Not necessarily. This model keeps the scheduled payment unchanged and adds the extra amount on top. Whether a lender recalculates a required payment after a principal reduction depends on the loan terms and servicing process.

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

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in p | 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 repayment | $ | 100 | 0 | 100000000
out sav | Estimated interest saved | $ | (pmt * yrs * 12 - p) - ((p + extra) * ceil(round(-ln(1 - (apr / 1200) * (p + extra) / (pmt + extra)) / ln(1 + apr / 1200), 6)) - p) | 2
out months | Estimated months to repay | months | ceil(round(-ln(1 - (apr / 1200) * (p + extra) / (pmt + extra)) / ln(1 + apr / 1200), 6)) | 0
out pmt | Original scheduled monthly payment | $ | round(p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)), 2) | 2
out int | Estimated interest with extra payments | $ | (pmt + extra) * months - p | 2