# Mortgage Calculator

> Estimate monthly house payments and see detailed amortization schedules for your loan.

**Category:** Finance
**Keywords:** mortgage, loan, home, interest, payment, finance, real estate, bank, amortization, math
**URL:** https://complete.tools/mortgage-calculator

## How it calculates

The formula used to calculate the monthly mortgage payment (M) is: M = P × (r(1 + r)^n) ÷ ((1 + r)^n - 1), where: P = principal loan amount, r = monthly interest rate (annual rate ÷ 12), and n = number of payments (loan term in years × 12). This formula derives from the present value of an annuity formula, which calculates the fixed monthly payment required to amortize a loan over its term. The relationship shows that as the interest rate or loan amount increases, the monthly payment also increases, affecting overall affordability.

## Who should use this

Real estate agents estimating monthly payments for clients, financial planners advising clients on mortgage options, accountants calculating tax implications of mortgage interest, and potential homebuyers assessing affordability based on their financial situation.

## Worked examples

Example 1: A homebuyer wants to purchase a home with a $250,000 loan at a 4% annual interest rate over 30 years. First, convert the interest rate: r = 0.04 ÷ 12 = 0.00333. The number of payments is n = 30 × 12 = 360. Plugging into the formula: M = 250,000 × (0.00333(1 + 0.00333)^(360)) ÷ ((1 + 0.00333)^(360) - 1) results in M ≈ $1,193.54. 

Example 2: An investor takes a $150,000 loan at a 5% interest rate for 15 years. First, convert the interest: r = 0.05 ÷ 12 = 0.00417 and n = 15 × 12 = 180. Using the formula: M = 150,000 × (0.00417(1 + 0.00417)^(180)) ÷ ((1 + 0.00417)^(180) - 1) results in M ≈ $1,187.43.

## Limitations

This calculator assumes a fixed interest rate for the entire loan term, which may not reflect reality for adjustable-rate mortgages. It does not account for additional costs such as private mortgage insurance (PMI), homeowner association (HOA) fees, or variable property taxes, which can significantly affect monthly payments. The precision of the calculation is limited to the number of decimal places used in the input values. Additionally, it assumes that borrowers will not make extra payments towards principal, potentially skewing the actual repayment timeline.

## FAQs

**Q:** How does changing the loan term affect my monthly payment?


**A:** Shortening the loan term generally increases the monthly payment but reduces the total interest paid over the life of the loan, while lengthening the term lowers the monthly payment but increases total interest costs.


**Q:** What impact does the interest rate have on the total cost of a mortgage?


**A:** A higher interest rate significantly increases the total cost of the mortgage due to greater interest accumulation over time, affecting overall affordability.


**Q:** Can this calculator incorporate additional fees like PMI or HOA?


**A:** No, this calculator focuses solely on principal, interest, and optional tax amounts; additional fees must be calculated separately and added to the monthly payment.


**Q:** How can I estimate my total payments over the life of the loan?


**A:** To find the total payments, multiply the monthly payment by the total number of payments (n). For example, if M is $1,200 and n is 360, total payments would be $1,200 × 360 = $432,000.

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