APR Calculator

Compute the true APR for a personal loan by factoring in origination and other finance charges. See the net amount disbursed, monthly payment, total interest, and finance charge before you sign.

Full original guide (expanded)

APR Calculator

Estimate the true annual percentage rate of a personal loan after origination and other finance charges. Enter principal, nominal rate, term, and fee treatment to see the effective APR, payments, and finance charge breakdown.

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

Loan details

$
%

Finance charges

%
$

Results

Effective APR 0.00%
Monthly payment $0.00
Net amount disbursed $0.00
Total of payments $0.00
Total interest $0.00
Finance charge (interest + fees) $0.00
Ready to calculate

Data Source and Methodology

The calculator applies Truth in Lending (Regulation Z) Appendix J methodology. Scheduled payments use the amortization formula; the effective APR is the internal rate of return that equates the present value of monthly payments to the net proceeds you receive after prepaid fees.

Formulas Used

Monthly rate: \( r = \dfrac{R}{12 \times 100} \)

Payment: \( \text{Payment} = \dfrac{P \cdot r}{1 - (1 + r)^{-n}} \) (if \( r = 0 \), then \( \text{Payment} = P / n \))

Net disbursed: \( \text{Net} = L - f_{\text{prepaid}} \)

APR (monthly IRR annualized): Find \( i \) so that \( \text{Net} = \sum_{k=1}^{n} \dfrac{\text{Payment}}{(1 + i)^{k}} \); then \( \text{APR} = (1 + i)^{12} - 1 \)

Interest: \( \text{Interest} = n \cdot \text{Payment} - P \)

Finance charge: \( \text{FinanceCharge} = \text{Interest} + f_{\text{prepaid}} + f_{\text{financed}} \)

Frequently Asked Questions

How does APR differ from the nominal rate?

The nominal rate determines the payment schedule. APR incorporates both that interest and mandatory finance charges, so it reflects the total annual cost of borrowing.

Which fees count toward finance charges?

Origination fees, discount points, and mandatory lender charges count. Optional add-ons, late fees, and government taxes generally do not. Refer to Regulation Z for specifics.

What if the payment is too small to amortize?

If the monthly payment cannot cover monthly interest, the balance grows. Increase the payment, shorten the term, or reduce the rate to compute a valid APR.

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: \( r = \dfrac{R}{12 \times 100} \) Payment: \( \text{Payment} = \dfrac{P \cdot r}{1 - (1 + r)^{-n}} \) (if \( r = 0 \), then \( \text{Payment} = P / n \)) Net disbursed: \( \text{Net} = L - f_{\text{prepaid}} \) APR (monthly IRR annualized): Find \( i \) so that \( \text{Net} = \sum_{k=1}^{n} \dfrac{\text{Payment}}{(1 + i)^{k}} \); then \( \text{APR} = (1 + i)^{12} - 1 \) Interest: \( \text{Interest} = n \cdot \text{Payment} - P \) Finance charge: \( \text{FinanceCharge} = \text{Interest} + f_{\text{prepaid}} + f_{\text{financed}} \)
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 test payoff strategies with the Loan Payoff Calculator.

APR Calculator

Estimate the true annual percentage rate of a personal loan after origination and other finance charges. Enter principal, nominal rate, term, and fee treatment to see the effective APR, payments, and finance charge breakdown.

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

Loan details

$
%

Finance charges

%
$

Results

Effective APR 0.00%
Monthly payment $0.00
Net amount disbursed $0.00
Total of payments $0.00
Total interest $0.00
Finance charge (interest + fees) $0.00
Ready to calculate

Data Source and Methodology

The calculator applies Truth in Lending (Regulation Z) Appendix J methodology. Scheduled payments use the amortization formula; the effective APR is the internal rate of return that equates the present value of monthly payments to the net proceeds you receive after prepaid fees.

Formulas Used

Monthly rate: \( r = \dfrac{R}{12 \times 100} \)

Payment: \( \text{Payment} = \dfrac{P \cdot r}{1 - (1 + r)^{-n}} \) (if \( r = 0 \), then \( \text{Payment} = P / n \))

Net disbursed: \( \text{Net} = L - f_{\text{prepaid}} \)

APR (monthly IRR annualized): Find \( i \) so that \( \text{Net} = \sum_{k=1}^{n} \dfrac{\text{Payment}}{(1 + i)^{k}} \); then \( \text{APR} = (1 + i)^{12} - 1 \)

Interest: \( \text{Interest} = n \cdot \text{Payment} - P \)

Finance charge: \( \text{FinanceCharge} = \text{Interest} + f_{\text{prepaid}} + f_{\text{financed}} \)

Frequently Asked Questions

How does APR differ from the nominal rate?

The nominal rate determines the payment schedule. APR incorporates both that interest and mandatory finance charges, so it reflects the total annual cost of borrowing.

Which fees count toward finance charges?

Origination fees, discount points, and mandatory lender charges count. Optional add-ons, late fees, and government taxes generally do not. Refer to Regulation Z for specifics.

What if the payment is too small to amortize?

If the monthly payment cannot cover monthly interest, the balance grows. Increase the payment, shorten the term, or reduce the rate to compute a valid APR.

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: \( r = \dfrac{R}{12 \times 100} \) Payment: \( \text{Payment} = \dfrac{P \cdot r}{1 - (1 + r)^{-n}} \) (if \( r = 0 \), then \( \text{Payment} = P / n \)) Net disbursed: \( \text{Net} = L - f_{\text{prepaid}} \) APR (monthly IRR annualized): Find \( i \) so that \( \text{Net} = \sum_{k=1}^{n} \dfrac{\text{Payment}}{(1 + i)^{k}} \); then \( \text{APR} = (1 + i)^{12} - 1 \) Interest: \( \text{Interest} = n \cdot \text{Payment} - P \) Finance charge: \( \text{FinanceCharge} = \text{Interest} + f_{\text{prepaid}} + f_{\text{financed}} \)
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 test payoff strategies with the Loan Payoff Calculator.

APR Calculator

Estimate the true annual percentage rate of a personal loan after origination and other finance charges. Enter principal, nominal rate, term, and fee treatment to see the effective APR, payments, and finance charge breakdown.

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

Loan details

$
%

Finance charges

%
$

Results

Effective APR 0.00%
Monthly payment $0.00
Net amount disbursed $0.00
Total of payments $0.00
Total interest $0.00
Finance charge (interest + fees) $0.00
Ready to calculate

Data Source and Methodology

The calculator applies Truth in Lending (Regulation Z) Appendix J methodology. Scheduled payments use the amortization formula; the effective APR is the internal rate of return that equates the present value of monthly payments to the net proceeds you receive after prepaid fees.

Formulas Used

Monthly rate: \( r = \dfrac{R}{12 \times 100} \)

Payment: \( \text{Payment} = \dfrac{P \cdot r}{1 - (1 + r)^{-n}} \) (if \( r = 0 \), then \( \text{Payment} = P / n \))

Net disbursed: \( \text{Net} = L - f_{\text{prepaid}} \)

APR (monthly IRR annualized): Find \( i \) so that \( \text{Net} = \sum_{k=1}^{n} \dfrac{\text{Payment}}{(1 + i)^{k}} \); then \( \text{APR} = (1 + i)^{12} - 1 \)

Interest: \( \text{Interest} = n \cdot \text{Payment} - P \)

Finance charge: \( \text{FinanceCharge} = \text{Interest} + f_{\text{prepaid}} + f_{\text{financed}} \)

Frequently Asked Questions

How does APR differ from the nominal rate?

The nominal rate determines the payment schedule. APR incorporates both that interest and mandatory finance charges, so it reflects the total annual cost of borrowing.

Which fees count toward finance charges?

Origination fees, discount points, and mandatory lender charges count. Optional add-ons, late fees, and government taxes generally do not. Refer to Regulation Z for specifics.

What if the payment is too small to amortize?

If the monthly payment cannot cover monthly interest, the balance grows. Increase the payment, shorten the term, or reduce the rate to compute a valid APR.

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: \( r = \dfrac{R}{12 \times 100} \) Payment: \( \text{Payment} = \dfrac{P \cdot r}{1 - (1 + r)^{-n}} \) (if \( r = 0 \), then \( \text{Payment} = P / n \)) Net disbursed: \( \text{Net} = L - f_{\text{prepaid}} \) APR (monthly IRR annualized): Find \( i \) so that \( \text{Net} = \sum_{k=1}^{n} \dfrac{\text{Payment}}{(1 + i)^{k}} \); then \( \text{APR} = (1 + i)^{12} - 1 \) Interest: \( \text{Interest} = n \cdot \text{Payment} - P \) Finance charge: \( \text{FinanceCharge} = \text{Interest} + f_{\text{prepaid}} + f_{\text{financed}} \)
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 test payoff strategies with the Loan Payoff Calculator.

Formulas

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

Version 0.1.0-draft
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).