Calculation Methodology & Mathematical Formulas
We believe in 100% transparent financial math. Below are the exact formulas, HUD guidelines, and amortization algorithms powering every calculation on this platform.
1. Monthly Principal & Interest (P&I) Formula
Standard fixed-rate mortgage payments are calculated using the continuous annuity amortization formula:
M = P × [ r(1 + r)^n ] / [ (1 + r)^n - 1 ]• M: Total monthly principal & interest payment
• P: Principal loan amount (for FHA, this includes the 1.75% Upfront MIP financed fee)
• r: Monthly interest rate (Annual Rate ÷ 100 ÷ 12)
• n: Total number of monthly payments (30 years × 12 = 360 payments)
2. FHA Upfront & Annual MIP Mathematical Logic
FHA loan calculations incorporate official HUD Mortgagee Letter rules:
Upfront MIP (UFMIP):
UFMIP = Base Loan Amount × 0.0175 (1.75%)
Total Financed FHA Balance = Base Loan Amount + UFMIP
Annual Monthly MIP:
Monthly MIP = (Base Loan Amount × Annual MIP Rate) ÷ 12
Where Annual MIP Rate = 0.55% for <5% down, or 0.50% for ≥5% down.
3. Conventional PMI Credit Score Risk Matrix
Conventional private mortgage insurance is modeled using empirical nationwide averages across major private mortgage insurers for 95% to 97% LTV loans:
| Credit Score Tier | Assigned Annual PMI Rate | Calculated Duration |
|---|---|---|
| 740+ FICO | 0.50% | Expires automatically at 80% LTV (~7-9 yrs) |
| 680 - 739 FICO | 0.75% | Expires automatically at 80% LTV (~7-9 yrs) |
| 620 - 679 FICO | 1.00% | Expires automatically at 80% LTV (~7-9 yrs) |
| 580 - 619 FICO | 1.35% | Expires automatically at 80% LTV (~7-9 yrs) |
4. 5-Year and 30-Year Cost Modeling Algorithms
To compute lifetime totals, our engine simulates a 360-month amortization schedule month-by-month:
- Tracks remaining monthly principal balances for both loans.
- Calculates exact cumulative interest paid at each milestone (Months 12, 60, 120, 240, 360).
- Applies automatic PMI drop-off once remaining balance hits 80% of original home value.
- Accounts for FHA MIP persistence (permanent vs. 11-year threshold depending on down payment).