Loan Prepayment Calculator

See how a one-time lump-sum prepayment shortens your loan term and cuts total interest. Enter balance, APR, term, and payment number to quantify payoff savings and months eliminated.

Loan amortization timeline

Loan payoff schedule with lump-sum prepayment
# Payment Interest Principal Lump sum Balance
Enter loan details to generate the schedule.

Full original guide (expanded)

Loan Prepayment Calculator

Enter your remaining balance, APR, term, and a one-time lump-sum payment to see the new payoff time and total interest saved. Perfect for planning bonus checks, tax refunds, or windfalls.

Author: Ugo Candido Reviewed by: Finance Content Editor Last updated: Category: Finance → Loans & Debt
$
%
$

Used to estimate the scheduled and new payoff dates.

Results

Monthly payment (unchanged) $0.00
Scheduled payoff time — Payoff date: —
Payoff after prepayment — Payoff date: —
Interest saved $0.00 Baseline interest: $0.00
Months eliminated 0
Prepayment details $0.00 Applied at payment #1
Ready to calculate

Data Source and Methodology

Payments follow the level-payment amortization formula used in Truth in Lending (Regulation Z) Appendix J. The lump-sum prepayment reduces the balance at the payment number you choose. After the lump is applied, the calculator keeps the scheduled payment unchanged and simulates the loan month by month until it pays off to compute interest savings and months eliminated.

Formulas Used

Monthly rate: \( r = \dfrac{\text{APR}}{12} \)

Scheduled payment: \( M = \dfrac{P \cdot r}{1 - (1 + r)^{-n}} \) (if \( r = 0 \) then \( M = P/n \))

After a lump sum \( L_{\text{ump}} \) at payment \( k \):

Remaining balance \( B_k = B_{k-1} - (M - B_{k-1} \cdot r) - L_{\text{ump}} \)

Monthly interest is recalculated each period as \( B_t \cdot r \) until the balance reaches zero.

Frequently Asked Questions

Will my lender reduce the required payment?

Usually no. After a lump sum you keep making the same payment and the term shortens. Some lenders allow a “recast” if you request it.

How do I choose the payment number?

Payment #1 applies the lump sum immediately. Larger payment numbers simulate applying the lump later in the loan, which saves less interest.

Do I have to pay extra every month?

No. This tool models a single lump sum while keeping the regular payment the same.

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[','\\]
','\
Formula (extracted text)
Monthly rate: \( r = \dfrac{\text{APR}}{12} \) Scheduled payment: \( M = \dfrac{P \cdot r}{1 - (1 + r)^{-n}} \) (if \( r = 0 \) then \( M = P/n \)) After a lump sum \( L_{\text{ump}} \) at payment \( k \): Remaining balance \( B_k = B_{k-1} - (M - B_{k-1} \cdot r) - L_{\text{ump}} \) Monthly interest is recalculated each period as \( B_t \cdot r \) until the balance reaches zero.
Variables and units
  • P = principal (loan amount) (currency)
  • r = periodic interest rate (annual rate ÷ payments per year) (1)
  • n = total number of payments (years × payments per year) (count)
  • M = periodic payment for principal + interest (currency)
  • T = property tax (annual or monthly depending on input) (currency)
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Need more help?

Explore more tools in the Loans & Debt hub, or visit the Loan Payoff Calculator to model recurring extra payments.

Loan Prepayment Calculator

Enter your remaining balance, APR, term, and a one-time lump-sum payment to see the new payoff time and total interest saved. Perfect for planning bonus checks, tax refunds, or windfalls.

Author: Ugo Candido Reviewed by: Finance Content Editor Last updated: Category: Finance → Loans & Debt
$
%
$

Used to estimate the scheduled and new payoff dates.

Results

Monthly payment (unchanged) $0.00
Scheduled payoff time — Payoff date: —
Payoff after prepayment — Payoff date: —
Interest saved $0.00 Baseline interest: $0.00
Months eliminated 0
Prepayment details $0.00 Applied at payment #1
Ready to calculate

Loan amortization timeline

Loan payoff schedule with lump-sum prepayment
# Payment Interest Principal Lump sum Balance
Enter loan details to generate the schedule.

Data Source and Methodology

Payments follow the level-payment amortization formula used in Truth in Lending (Regulation Z) Appendix J. The lump-sum prepayment reduces the balance at the payment number you choose. After the lump is applied, the calculator keeps the scheduled payment unchanged and simulates the loan month by month until it pays off to compute interest savings and months eliminated.

Formulas Used

Monthly rate: \( r = \dfrac{\text{APR}}{12} \)

Scheduled payment: \( M = \dfrac{P \cdot r}{1 - (1 + r)^{-n}} \) (if \( r = 0 \) then \( M = P/n \))

After a lump sum \( L_{\text{ump}} \) at payment \( k \):

Remaining balance \( B_k = B_{k-1} - (M - B_{k-1} \cdot r) - L_{\text{ump}} \)

Monthly interest is recalculated each period as \( B_t \cdot r \) until the balance reaches zero.

Frequently Asked Questions

Will my lender reduce the required payment?

Usually no. After a lump sum you keep making the same payment and the term shortens. Some lenders allow a “recast” if you request it.

How do I choose the payment number?

Payment #1 applies the lump sum immediately. Larger payment numbers simulate applying the lump later in the loan, which saves less interest.

Do I have to pay extra every month?

No. This tool models a single lump sum while keeping the regular payment the same.

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[','\\]
','\
Formula (extracted text)
Monthly rate: \( r = \dfrac{\text{APR}}{12} \) Scheduled payment: \( M = \dfrac{P \cdot r}{1 - (1 + r)^{-n}} \) (if \( r = 0 \) then \( M = P/n \)) After a lump sum \( L_{\text{ump}} \) at payment \( k \): Remaining balance \( B_k = B_{k-1} - (M - B_{k-1} \cdot r) - L_{\text{ump}} \) Monthly interest is recalculated each period as \( B_t \cdot r \) until the balance reaches zero.
Variables and units
  • P = principal (loan amount) (currency)
  • r = periodic interest rate (annual rate ÷ payments per year) (1)
  • n = total number of payments (years × payments per year) (count)
  • M = periodic payment for principal + interest (currency)
  • T = property tax (annual or monthly depending on input) (currency)
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Need more help?

Explore more tools in the Loans & Debt hub, or visit the Loan Payoff Calculator to model recurring extra payments.

Loan Prepayment Calculator

Enter your remaining balance, APR, term, and a one-time lump-sum payment to see the new payoff time and total interest saved. Perfect for planning bonus checks, tax refunds, or windfalls.

Author: Ugo Candido Reviewed by: Finance Content Editor Last updated: Category: Finance → Loans & Debt
$
%
$

Used to estimate the scheduled and new payoff dates.

Results

Monthly payment (unchanged) $0.00
Scheduled payoff time — Payoff date: —
Payoff after prepayment — Payoff date: —
Interest saved $0.00 Baseline interest: $0.00
Months eliminated 0
Prepayment details $0.00 Applied at payment #1
Ready to calculate

Loan amortization timeline

Loan payoff schedule with lump-sum prepayment
# Payment Interest Principal Lump sum Balance
Enter loan details to generate the schedule.

Data Source and Methodology

Payments follow the level-payment amortization formula used in Truth in Lending (Regulation Z) Appendix J. The lump-sum prepayment reduces the balance at the payment number you choose. After the lump is applied, the calculator keeps the scheduled payment unchanged and simulates the loan month by month until it pays off to compute interest savings and months eliminated.

Formulas Used

Monthly rate: \( r = \dfrac{\text{APR}}{12} \)

Scheduled payment: \( M = \dfrac{P \cdot r}{1 - (1 + r)^{-n}} \) (if \( r = 0 \) then \( M = P/n \))

After a lump sum \( L_{\text{ump}} \) at payment \( k \):

Remaining balance \( B_k = B_{k-1} - (M - B_{k-1} \cdot r) - L_{\text{ump}} \)

Monthly interest is recalculated each period as \( B_t \cdot r \) until the balance reaches zero.

Frequently Asked Questions

Will my lender reduce the required payment?

Usually no. After a lump sum you keep making the same payment and the term shortens. Some lenders allow a “recast” if you request it.

How do I choose the payment number?

Payment #1 applies the lump sum immediately. Larger payment numbers simulate applying the lump later in the loan, which saves less interest.

Do I have to pay extra every month?

No. This tool models a single lump sum while keeping the regular payment the same.

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[','\\]
','\
Formula (extracted text)
Monthly rate: \( r = \dfrac{\text{APR}}{12} \) Scheduled payment: \( M = \dfrac{P \cdot r}{1 - (1 + r)^{-n}} \) (if \( r = 0 \) then \( M = P/n \)) After a lump sum \( L_{\text{ump}} \) at payment \( k \): Remaining balance \( B_k = B_{k-1} - (M - B_{k-1} \cdot r) - L_{\text{ump}} \) Monthly interest is recalculated each period as \( B_t \cdot r \) until the balance reaches zero.
Variables and units
  • P = principal (loan amount) (currency)
  • r = periodic interest rate (annual rate ÷ payments per year) (1)
  • n = total number of payments (years × payments per year) (count)
  • M = periodic payment for principal + interest (currency)
  • T = property tax (annual or monthly depending on input) (currency)
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Need more help?

Explore more tools in the Loans & Debt hub, or visit the Loan Payoff Calculator to model recurring extra payments.

Formulas

(Formulas preserved from original page content, if present.)

Version 1.5.0
Citations

Add authoritative sources relevant to this calculator (standards bodies, manuals, official docs).

Changelog
  • 0.1.0-draft — 2026-01-19: Initial draft (review required).