# Amortization Calculator

> Calculate payment amounts, total interest, and schedules with optional extra payments.

**Category:** Finance
**Keywords:** amortization, loan, payment, schedule, finance, interest
**URL:** https://complete.tools/amortization-calculator

## How it calculates

The monthly payment (M) can be calculated using the formula: M = P × (r(1 + r)^n) ÷ ((1 + r)^n - 1), where: P = principal loan amount, r = monthly interest rate (annual rate ÷ 12), and n = total number of payments (loan term in months). This formula derives from the concept of present value of an annuity, where the loan is considered an annuity that needs to be paid off over time. The relationship shows that as the interest rate increases, the monthly payment also increases, and as the loan term lengthens, the payment decreases. The amortization schedule is generated by tracking the remaining balance after each payment, calculating interest, and determining the amount applied to the principal.

## Who should use this

Mortgage brokers analyzing loan options for clients, real estate agents helping buyers understand financing costs, accountants preparing financial statements that include loan amortization, and financial planners assisting clients in managing debt repayment strategies.

## Worked examples

Example 1: A homeowner takes a $200,000 mortgage with a 4% annual interest rate for 30 years. The monthly interest rate (r) is 0.04 ÷ 12 = 0.00333, and the number of payments (n) is 30 × 12 = 360. Using the formula, M = 200,000 × (0.00333(1 + 0.00333)^360) ÷ ((1 + 0.00333)^360 - 1), M = $954.83. The total interest paid over the life of the loan is $954.83 × 360 - $200,000 = $143,739. Example 2: A car loan of $25,000 at an annual interest rate of 5% for 5 years. Monthly interest rate (r) is 0.05 ÷ 12 = 0.00417, and n is 5 × 12 = 60. M = 25,000 × (0.00417(1 + 0.00417)^60) ÷ ((1 + 0.00417)^60 - 1), M = $471.78. The total interest paid is $471.78 × 60 - $25,000 = $2,306.80.

## Limitations

The calculator assumes a fixed interest rate throughout the loan term, which may not apply to variable-rate loans. It also does not account for additional fees or taxes that may be included in actual mortgage payments. The precision of calculations may be limited by rounding of interest rates and payment amounts, and results may become less accurate for very short loan terms or loans with large balloon payments. Additionally, it assumes that all payments are made on time and does not consider late fees or changes in payment frequency.

## FAQs

**Q:** How does the calculator handle extra payments?


**A:** The calculator allows users to input extra payments, which can be applied to the principal. This reduces the total interest paid and shortens the loan term based on the timing and frequency of these payments.


**Q:** What happens if I change the interest rate mid-loan?


**A:** The calculator does not adjust for changes in interest rates after the loan has started. It is designed for fixed-rate calculations unless manually updated by the user.


**Q:** Can I see the impact of refinancing with this tool?


**A:** Yes, users can input new loan terms from refinancing to compare potential new monthly payments and total interest against the original loan, but it will not automatically calculate the costs of refinancing itself.


**Q:** How is the total interest calculated over the loan term?


**A:** Total interest is calculated by taking the total amount paid over the loan term (monthly payment × number of payments) and subtracting the principal amount borrowed.

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*Generated from [complete.tools/amortization-calculator](https://complete.tools/amortization-calculator)*