A fixed-rate mortgage spreads your loan into equal monthly payments through the amortization formula M = P·r(1+r)ⁿ / ((1+r)ⁿ−1). Each payment covers the month's interest first, with the rest chipping away at the principal — so early payments are mostly interest and later ones mostly principal. Two levers dominate the cost: the interest rate and the term. A lower rate or shorter term cuts the total interest sharply, which over 30 years and hundreds of payments can mean saving more than the size of the loan itself.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: the standard fixed-rate amortization formula. Not financial advice.
The mortgage equations
Convert the annual percentage rate to a monthly decimal rate (divide by 12 and by 100), and the term to a number of months. The amortization factor r(1+r)ⁿ/((1+r)ⁿ−1) turns the principal into a level monthly payment that fully clears the loan over n months. Multiply that payment by n for the total paid, and subtract the principal to see how much of it was interest. If the rate is 0%, the payment is simply P/n.
Worked example — a 30-year home loan
Scenario: You borrow 300,000 at 6% annual interest over 30 years.
The payment is about 1,798.65 a month. Over 360 payments that's 647,514 in total, so the interest alone is roughly 347,514 — more than the amount borrowed. Drop the rate to 5% and the payment falls to about 1,610 (interest ≈ 279,767); a 1-point rise to 7% pushes it to about 1,996 (interest ≈ 418,527). Shortening to a 15-year term raises the monthly payment but slashes the lifetime interest, the clearest lever for paying less overall.
Frequently Asked Questions
M = P·r(1+r)ⁿ/((1+r)ⁿ−1), r = annual%/12/100, n = years×12. 300k at 6% over 30 yr ≈ 1,798.65.
M×n − P. On 300k at 6% over 30 yr ≈ 347,514 — more than the loan itself.
Yes — higher monthly payment but far less total interest, since you borrow for less time.
A lot. 6%→7% on a 300k/30-yr loan adds ~200/month and ~70k in total interest.
No — principal & interest only. Add property tax, insurance and PMI for the full (PITI) payment.