Mortgage Payment Formula Explained
A mortgage is an amortizing loan: each monthly payment covers that month's interest on the remaining balance plus a portion of the principal. The payment amount is the same every month for a fixed-rate mortgage, but the split between interest and principal changes dramatically over the loan's life.
Understanding the mortgage payment formula helps you evaluate affordability, compare 15-year vs 30-year terms, calculate the benefit of a larger down payment, and understand what you are actually paying for in the early years of a mortgage.
The Mortgage Payment Formula
M = L × [r(1+r)^n] / [(1+r)^n - 1] Where: M = monthly payment (principal + interest) L = loan amount (home price minus down payment) r = monthly rate = annual rate ÷ 12 n = total payments = years × 12 Example: $350,000 home, $70,000 down (20%), 7%, 30yr: L = $280,000 r = 0.07 ÷ 12 = 0.005833 n = 360 M ≈ $1,863/month Total paid: $670,768 Total interest: $390,768 Same home at 15 years (6.5%): M ≈ $2,440/month Total interest: $159,200 (saves $231,568)
Down Payment and Its Effect
The down payment directly reduces the loan amount. A larger down payment means a smaller loan, lower monthly payments, and far less total interest. Additionally, a 20% or greater down payment typically eliminates the requirement for PMI (Private Mortgage Insurance), which can cost 0.5–1% of the loan amount per year.
On a $350,000 home: 10% down ($35,000) leaves a $315,000 loan and likely requires PMI. 20% down ($70,000) leaves a $280,000 loan with no PMI. The difference in total interest over 30 years is about $44,000 — plus the PMI savings of roughly $15,000–$30,000 over the years before 20% equity is reached.
What Is Not Included in the Payment Formula
The formula calculates only principal and interest. Your actual monthly payment includes: property taxes (typically 1–2% of home value annually, escrowed monthly), homeowner's insurance ($1,000–$3,000/year, escrowed monthly), PMI if applicable ($1,000–$3,000/year), and HOA fees if in a community.
For a $350,000 home, taxes + insurance alone might add $400–$700/month on top of the principal and interest payment. Budget for the full PITI (Principal, Interest, Taxes, Insurance) when assessing affordability.
Quick Tips
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Compare 30-year vs 15-year with this calculator — the interest savings on a 15-year are often $150,000–$250,000+.
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A 1% rate difference on a $300,000 mortgage over 30 years is about $60,000 in total interest.
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Paying one extra mortgage payment per year cuts ~4 years off a 30-year mortgage.
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Get quotes from 3+ lenders — rate differences of 0.25–0.5% are common and worth the 30 minutes of effort.
Frequently Asked Questions
What is a good mortgage rate?
Mortgage rates change daily based on economic conditions, Federal Reserve policy, and your credit profile. A 'good' rate is one that is competitive relative to current market rates. Track weekly averages from sources like Freddie Mac's Primary Mortgage Market Survey. Focus on APR (which includes fees) for a true comparison.
Should I choose a 15-year or 30-year mortgage?
The 15-year has a lower rate, builds equity faster, and saves enormous interest. The 30-year has lower required payments, giving more monthly cash flow flexibility. A common approach: take a 30-year mortgage but pay it like a 15-year when possible, giving you the flexibility to cut back if needed.
How does my credit score affect my mortgage rate?
Significantly. A score of 760+ typically gets the best rates. A score of 680–700 might add 0.5–1% to your rate. On a $300,000 mortgage for 30 years, 1% more rate = about $60,000 more in total interest. Improving your score before applying can be worth thousands.
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