Learning goals
- Explain how rate, term, and loan amount drive a fixed mortgage payment
- Separate principal-and-interest (P&I) from taxes, insurance, and other escrow items
- See why a longer term lowers the monthly payment but raises total interest
What your mortgage payment really covers
A fixed-rate mortgage is sized so equal payments pay off the loan by the end of the term if you stay on schedule. Each month, part of the payment covers interest on what you still owe; the rest reduces principal.
Lenders often quote the principal-and-interest (P&I) payment from the amortization formula. Your full housing payment may also include property taxes, homeowners insurance, and sometimes mortgage insurance (PMI) or HOA dues — often collected in escrow. That full stack is sometimes called PITI (principal, interest, taxes, insurance).
Changing the term, rate, or down payment changes P&I immediately. Escrow items can change over time even when the loan rate is fixed.
Fixed mortgage payment (P&I)
PMT = P × r(1 + r)^n / ((1 + r)^n − 1)
P is the loan amount (price minus down payment, plus financed fees if any), r is the monthly rate (APR ÷ 12 as a decimal), and n is the number of monthly payments (years × 12). This PMT is principal and interest only.
First-month interest
interest = balance × r
Principal portion = PMT − interest. New balance = old balance − principal portion. Early years are interest-heavy on long mortgages.
Example 1 — Estimate a monthly P&I payment
Given
Home price $300,000.00 20% down, 6% APR, 30-year fixed. Approximate monthly P&I.
Steps
- Loan principal P = 300,000 × 0.80 = $240,000.00.
- Monthly rate r = 0.06 / 12 = 0.005; n = 30 × 12 = 360.
- Using the payment formula, PMT ≈ $1,438.92.
Answer
Principal and interest are about $1,439.00 per month.
Tip: Taxes and insurance can easily add hundreds more to the escrow payment.
Example 2 — First month split
Given
Same loan: balance $240,000.00 r = 0.005, payment ≈ $1,438.92.
Steps
- Interest month 1 = 240,000 × 0.005 = $1,200.00.
- Principal month 1 ≈ 1,438.92 − 1,200 = $238.92.
- Ending balance ≈ 240,000 − 238.92 = $239,761.08.
Answer
Month 1 is mostly interest: about $1,200.00 interest vs $239.00 principal.
Tip: On a 30-year loan, early payments feel interest-heavy even when you are on track.
Example 3 — Shorter term vs lower payment
Given
Same $240,000.00 at 6%, compare 30-year vs 15-year approximate P&I.
Steps
- 30-year (n = 360): PMT ≈ $1,439.00.
- 15-year (n = 180): PMT ≈ $2,025.00.
- The 15-year payment is higher each month, but you pay interest for far fewer years — total interest falls sharply.
Answer
Shorter terms raise the monthly bill and cut lifetime interest.
Tip: Compare total interest and cash-flow fit, not payment size alone.
Confusing the advertised rate payment with the full monthly draft
Common mistake
Budget only the P&I quote and ignore taxes, insurance, or PMI.
Better approach
Ask for the estimated total monthly payment including escrow. Rate locks fix P&I; escrow can still adjust at closing and at annual reviews.
Check your understanding
1.Price $250,000.00 with 10% down. What is the loan principal?
Answer: 250,000 × 0.90 = $225,000.00.
2.APR 4.8% paid monthly. What is r?
Answer: 0.048 / 12 = 0.004.
3.Balance $200,000.00 r = 0.005, payment $1,200.00. Month-1 interest and principal?
Answer: Interest $1,000.00; principal $200.00.
4.Why might two homes with the same P&I have different full payments?
Answer: Different taxes, insurance, PMI, or HOA amounts in escrow.
Key takeaways
- Fixed P&I comes from principal, periodic rate, and number of payments.
- Early mortgage payments are mostly interest; principal share grows over time.
- Full housing cost often includes taxes and insurance on top of P&I.
- Shorter terms cost more per month and usually less interest overall.