Loan Payment (Amortization) Formula Calculator

This calculator is designed to help users calculate monthly loan payments based on the amortization formula. It's perfect for anyone looking to understand their loan structure and payment schedule.

Loan Calculator

Calculation Results

Monthly Payment $0.00

Data Source and Methodology

All calculations are based on the standard amortization formula. For more details, please refer to authoritative financial documents.

The Formula Explained

\( M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \)

Where \( M \) is the monthly payment, \( P \) is the principal loan amount, \( r \) is the monthly interest rate, and \( n \) is the number of payments.

Glossary of Terms

How It Works: A Step-by-Step Example

Consider a $10,000 loan with a 5% annual interest rate over 15 years. The monthly interest rate is 0.4167%. Using the formula, the monthly payment can be calculated as $79.08.

Frequently Asked Questions (FAQ)

What is loan amortization?

Loan amortization is the process of spreading out a loan into equal payments over its term.

How do I calculate the monthly payment?

Use the formula provided above, or use this calculator for an accurate computation.

What happens if I pay off my loan early?

Paying off a loan early can reduce the total interest paid over the life of the loan.

How is the interest calculated in each payment?

Each payment consists of both principal and interest, with the interest portion reducing over time.

Can the interest rate change over time?

This depends on the loan type; fixed-rate loans have constant rates, while variable-rate loans can change.

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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)
\( M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \) Where \( M \) is the monthly payment, \( P \) is the principal loan amount, \( r \) is the monthly interest rate, and \( n \) is the number of payments.
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)
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
, ', svg: { fontCache: 'global' } };

Loan Payment (Amortization) Formula Calculator

This calculator is designed to help users calculate monthly loan payments based on the amortization formula. It's perfect for anyone looking to understand their loan structure and payment schedule.

Loan Calculator

Calculation Results

Monthly Payment $0.00

Data Source and Methodology

All calculations are based on the standard amortization formula. For more details, please refer to authoritative financial documents.

The Formula Explained

\( M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \)

Where \( M \) is the monthly payment, \( P \) is the principal loan amount, \( r \) is the monthly interest rate, and \( n \) is the number of payments.

Glossary of Terms

How It Works: A Step-by-Step Example

Consider a $10,000 loan with a 5% annual interest rate over 15 years. The monthly interest rate is 0.4167%. Using the formula, the monthly payment can be calculated as $79.08.

Frequently Asked Questions (FAQ)

What is loan amortization?

Loan amortization is the process of spreading out a loan into equal payments over its term.

How do I calculate the monthly payment?

Use the formula provided above, or use this calculator for an accurate computation.

What happens if I pay off my loan early?

Paying off a loan early can reduce the total interest paid over the life of the loan.

How is the interest calculated in each payment?

Each payment consists of both principal and interest, with the interest portion reducing over time.

Can the interest rate change over time?

This depends on the loan type; fixed-rate loans have constant rates, while variable-rate loans can change.

```
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)
\( M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \) Where \( M \) is the monthly payment, \( P \) is the principal loan amount, \( r \) is the monthly interest rate, and \( n \) is the number of payments.
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)
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
]], displayMath: [['\\[','\\]']] }, svg: { fontCache: 'global' } };, svg: { fontCache: 'global' } };

Loan Payment (Amortization) Formula Calculator

This calculator is designed to help users calculate monthly loan payments based on the amortization formula. It's perfect for anyone looking to understand their loan structure and payment schedule.

Loan Calculator

Calculation Results

Monthly Payment $0.00

Data Source and Methodology

All calculations are based on the standard amortization formula. For more details, please refer to authoritative financial documents.

The Formula Explained

\( M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \)

Where \( M \) is the monthly payment, \( P \) is the principal loan amount, \( r \) is the monthly interest rate, and \( n \) is the number of payments.

Glossary of Terms

How It Works: A Step-by-Step Example

Consider a $10,000 loan with a 5% annual interest rate over 15 years. The monthly interest rate is 0.4167%. Using the formula, the monthly payment can be calculated as $79.08.

Frequently Asked Questions (FAQ)

What is loan amortization?

Loan amortization is the process of spreading out a loan into equal payments over its term.

How do I calculate the monthly payment?

Use the formula provided above, or use this calculator for an accurate computation.

What happens if I pay off my loan early?

Paying off a loan early can reduce the total interest paid over the life of the loan.

How is the interest calculated in each payment?

Each payment consists of both principal and interest, with the interest portion reducing over time.

Can the interest rate change over time?

This depends on the loan type; fixed-rate loans have constant rates, while variable-rate loans can change.

```
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)
\( M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \) Where \( M \) is the monthly payment, \( P \) is the principal loan amount, \( r \) is the monthly interest rate, and \( n \) is the number of payments.
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)
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