Monthly Payment Formula (Principal & Interest)
The standard fixed-rate mortgage payment formula is the foundation of every calculator on this site. This formula computes the fixed monthly payment required to fully amortize a loan over a given term at a fixed interest rate. It is the same formula used by Fannie Mae, Freddie Mac, and every TILA-compliant lender in the United States.
M = Monthly payment (principal + interest)
P = Principal loan amount (home price minus down payment)
r = Monthly interest rate (annual rate ÷ 12 ÷ 100)
n = Total number of monthly payments (years × 12)
Worked Example
For a $300,000 loan at 6.5% annual rate over 30 years:
- P = $300,000
- r = 6.5% ÷ 12 ÷ 100 = 0.005417
- n = 30 × 12 = 360 payments
- M = $300,000 × [0.005417 × (1.005417)360] / [(1.005417)360 − 1]
- M = $300,000 × [0.005417 × 6.9916] / [6.9916 − 1]
- M = $300,000 × 0.037876 / 5.9916
- M = $1,896.20 per month
Try this yourself using our mortgage payment calculator.
Amortization Schedule Formula
An amortization schedule breaks each monthly payment into the interest portion and the principal portion. In the early years, most of each payment goes toward interest. Over time, the balance shifts toward principal.
Principalmonth = M − Interestmonth
New Balance = Balance − Principalmonth
Worked Example (Month 1)
Using the $300,000 loan at 6.5% from above:
- Interest (Month 1) = $300,000 × 0.005417 = $1,625.00
- Principal (Month 1) = $1,896.20 − $1,625.00 = $271.20
- Remaining Balance = $300,000 − $271.20 = $299,728.80
In month 1, 85.7% of the payment goes to interest and only 14.3% to principal. By month 180 (halfway), approximately 50% goes to each. By month 360, nearly the entire payment is principal. View a full schedule with our amortization schedule calculator.
PITI — Total Monthly Payment Formula
Your actual monthly mortgage obligation includes more than just principal and interest. Lenders qualify you based on PITI — the total of all four components:
Property Tax = (Home Value × Tax Rate) ÷ 12
Insurance = Annual Premium ÷ 12
PMI = (Loan Amount × PMI Rate) ÷ 12 (only if LTV > 80%)
Worked Example
For a $350,000 home, $280,000 loan, 1.1% property tax, $1,800/yr insurance:
- P&I = $1,896.20 (from formula above, adjusted for $280,000 loan)
- Property Tax = ($350,000 × 0.011) / 12 = $320.83
- Insurance = $1,800 / 12 = $150.00
- PMI = ($280,000 × 0.005) / 12 = $116.67 (at 80% LTV, PMI just at threshold)
- Total PITI = $2,483.70
Debt-to-Income Ratio (DTI) Formula
DTI is the primary metric lenders use to determine how much you can borrow. There are two types:
Maximum DTI by Loan Type
| Loan Type | Max Front-End | Max Back-End |
|---|---|---|
| Conventional | 28% | 36-45% |
| FHA | 31% | 43-57% |
| VA | No limit | 41% guideline |
| USDA | 29% | 41% |
Worked Example
Income $7,000/month, PITI $1,900, car $400, student loans $250:
- Front-End DTI = $1,900 / $7,000 = 27.1% (under 28% — passes conventional)
- Back-End DTI = ($1,900 + $400 + $250) / $7,000 = 36.4% (under 45% — passes)
Calculate your DTI with our DTI calculator.
Loan-to-Value Ratio (LTV) Formula
LTV measures how much of the property value is financed by the loan. It determines PMI requirements and affects your interest rate.
Key LTV Thresholds
- 80% or below: No PMI required on conventional loans
- 80.01% - 95%: PMI required, rates vary by credit score
- 95.01% - 96.5%: Maximum for conventional (97%) and FHA (96.5%)
- 100%: VA and USDA loans allow zero down payment
Check your LTV with our LTV calculator.
Private Mortgage Insurance (PMI) Calculation
PMI is required on conventional loans when LTV exceeds 80%. The annual premium is a percentage of the original loan amount, varying by LTV and credit score.
Typical PMI Rates by Credit Score
| Credit Score | 95% LTV | 90% LTV | 85% LTV |
|---|---|---|---|
| 760+ | 0.41% | 0.19% | 0.15% |
| 720-759 | 0.54% | 0.30% | 0.23% |
| 680-719 | 0.72% | 0.47% | 0.37% |
| 640-679 | 1.08% | 0.65% | 0.50% |
| 620-639 | 1.24% | 0.83% | 0.65% |
PMI automatically cancels when LTV reaches 78% through normal payments (Homeowners Protection Act of 1998). You can request cancellation at 80%. Use our PMI calculator to see your costs.
Affordability Formula
To determine the maximum home price you can afford, we work backward from your income using the 28% front-end DTI rule:
Worked Example
Annual income $100,000 ($8,333/month), 6.5% rate, 30 years, 1.1% tax, $150/mo insurance:
- Max PITI = $8,333 × 0.28 = $2,333
- Estimated tax + insurance = ~$470/mo (varies by price)
- Max P&I = $2,333 − $470 = $1,863
- Max Loan (using inverse formula) = ~$295,000
- With 20% down, Max Home Price = $295,000 / 0.80 = ~$369,000
Try our affordability calculator or home price calculator.
Refinance Break-Even Formula
The break-even point tells you how many months it takes for your monthly savings to recoup the closing costs of refinancing.
Monthly Savings = Old Payment − New Payment
Worked Example
Current payment $2,100, new payment $1,850, closing costs $6,000:
- Monthly Savings = $2,100 − $1,850 = $250
- Break-Even = $6,000 / $250 = 24 months
If you plan to stay in the home more than 24 months, refinancing makes financial sense. Use our break-even calculator or refinance calculator.
Extra Payments & Early Payoff Formula
Extra payments reduce the principal balance faster, which reduces future interest charges. There is no single closed-form formula — the calculation requires an iterative amortization loop where the extra payment is subtracted from principal each month.
Principal = M − Interest + Extra Payment
New Balance = Balance − Principal
Impact Example
On a $300,000 loan at 6.5% for 30 years (payment $1,896.20):
- $100 extra/month: Saves $66,290 in interest, pays off 5 years 2 months early
- $200 extra/month: Saves $108,754 in interest, pays off 8 years 7 months early
- $500 extra/month: Saves $181,085 in interest, pays off 14 years 10 months early
- Biweekly payments: 26 half-payments = 13 full payments per year, saves ~$54,000
Model your scenario with our extra payments calculator.
ARM Rate Adjustment Formula
Adjustable-rate mortgages recalculate the interest rate at specified intervals. The new rate is determined by adding a margin to an index rate, subject to caps.
Subject to: Initial Cap, Periodic Cap, Lifetime Cap
Index = SOFR (Secured Overnight Financing Rate), current benchmark
Margin = Lender's fixed markup (typically 2.75%)
Caps (5/2/5) = 5% max first adjustment, 2% per subsequent, 5% lifetime
Example: 5/1 ARM
Initial rate 5.5%, margin 2.75%, SOFR = 4.0% at adjustment, caps 5/2/5:
- Calculated rate = 4.0% + 2.75% = 6.75%
- Initial cap check: 6.75% − 5.5% = 1.25% (under 5% cap — passes)
- New rate = 6.75%
- Payment recalculated on remaining balance for remaining term
Model ARM scenarios with our ARM calculator.
FHA Mortgage Insurance Premium (MIP) Calculation
FHA loans require both an upfront premium and an annual premium, regardless of LTV ratio.
For loans ≤ $726,200, LTV > 95%, term > 15 years: 0.55% annually
For loans ≤ $726,200, LTV ≤ 95%, term > 15 years: 0.50% annually
Worked Example
Home price $350,000, 3.5% down ($12,250), base loan $337,750:
- Upfront MIP = $337,750 × 0.0175 = $5,910.63 (rolled into loan)
- Total loan = $337,750 + $5,910.63 = $343,660.63
- Monthly MIP = ($343,660.63 × 0.0055) / 12 = $157.51
Note: FHA MIP for 30-year loans with LTV > 90% lasts the life of the loan and cannot be cancelled. Calculate with our FHA loan calculator.
VA Funding Fee Calculation
VA loans charge a one-time funding fee instead of mortgage insurance. The fee varies by down payment, usage, and military category.
VA Funding Fee Rates (Purchase, Regular Military)
| Down Payment | First Use | Subsequent Use |
|---|---|---|
| 0% (zero down) | 2.15% | 3.30% |
| 5% - 9.99% | 1.50% | 1.50% |
| 10% or more | 1.25% | 1.25% |
Worked Example
Home price $400,000, zero down, first-time use:
- Funding Fee = $400,000 × 0.0215 = $8,600
- Total loan = $400,000 + $8,600 = $408,600
- Monthly P&I (at 6.0%, 30yr) = $2,449.71
Veterans receiving VA disability compensation are exempt from the funding fee. Calculate with our VA loan calculator.