1. What is the Mortgage Interest Rate Formula?

The mortgage payment formula calculates the fixed monthly payment (PMT) required to fully amortize a loan of amount P over n months at a monthly interest rate r.

2. How Does the Calculator Work?

The calculator solves for r in the equation:

Where:

• \( PMT \) — Monthly payment amount
• \( P \) — Principal loan amount
• \( r \) — Monthly interest rate (decimal)
• \( n \) — Number of monthly payments

Explanation: The calculator uses numerical methods (Newton-Raphson) to solve for the interest rate when all other variables are known.

3. Importance of Accurate Rate Calculation

Details: Knowing the effective interest rate helps borrowers compare loan offers, understand the true cost of borrowing, and make informed financial decisions.

4. Using the Calculator

Tips: Enter your monthly payment amount, total loan amount, and loan term in months. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why can't the rate be calculated directly?
A: The equation is transcendental and cannot be solved algebraically for r, requiring numerical methods.

Q2: How accurate is this calculator?
A: It's accurate to within 0.0001 (0.01%) for standard mortgage terms.

Q3: Does this include taxes and insurance?
A: No, this calculates only the principal and interest portion of the payment.

Q4: What if my payments are bi-weekly?
A: Convert bi-weekly payments to monthly by multiplying by 26 and dividing by 12.

Q5: Why does my calculated rate differ from my APR?
A: APR includes fees and other loan costs, while this calculates the pure interest rate.