Financial Methodology & Formulas
Transparency is the foundation of advisor-grade financial planning. Below is the complete mathematical framework, variables, and formulas used by our decision engines.
1. Standard Mortgage Amortization
Our calculators model standard monthly amortizing loans using the fixed-rate payment equation. Interest is calculated on the outstanding balance monthly rather than daily.
M = P × [ r(1 + r)ⁿ ] / [ (1 + r)ⁿ - 1 ]
Each monthly payment is broken down into interest (outstanding balance times the monthly interest rate) and principal (the remaining payment amount). The balance decreases iteratively month by month.
2. Refinance Break-Even Analysis
Refinancing is modeled by comparing the monthly payment of the existing loan against the proposed new loan. The break-even point is defined as the number of months required for cumulative monthly savings to offset the closing costs.
Break-Even Month = ⌈ Upfront Closing Costs / Monthly Savings ⌉
If closing costs are rolled into the new loan amount, they are added to the principal ($P$), increasing the new monthly payment and reducing the actual monthly savings.
3. Private Mortgage Insurance (PMI) Scheduling
Under the Homeowners Protection Act of 1998, conventional mortgage lenders must automatically terminate PMI once the loan-to-value (LTV) ratio reaches 78% of the original purchase value, assuming payments are current. Borrowers may request manual cancellation once the loan reaches 80% LTV.
We calculate the PMI drop month by tracing the amortization table month-by-month. Once the outstanding balance declines below 80% of the original home price, the platform records the milestone date and subtracts the PMI cost from subsequent monthly totals.
4. Debt-to-Income (DTI) lending criteria
Lenders evaluate risk using two primary DTI ratios:
- Front-End DTI (Housing Ratio): Monthly housing expenses (Principal, Interest, Property Taxes, Insurance, HOA) divided by gross monthly income. Traditionally capped at 28%.
- Back-End DTI (Total Debt Ratio): Total recurring monthly debts (Housing costs plus credit cards, auto loans, student loans, and child support) divided by gross monthly income. Capped at 36% for conventional qualification.
Our DTI gauge models these limits, categorizing risk as Comfortable (≤ 28%), Stretch (28.1% - 36%), and Danger (> 36%).
Underwriting Review & Compliance
Our math engine is modeled on guidelines published by the Federal National Mortgage Association (Fannie Mae) and Federal Home Loan Mortgage Corporation (Freddie Mac). Calculations are reviewed periodically by compliance officers.