PITI Mortgage & Amortization Calculator
Calculate your complete monthly housing payment (Principal, Interest, Property Taxes, Homeowners Insurance, and PMI). Model extra monthly principal payments to calculate exact interest savings and loan payoff acceleration.
Loan Details & Property Expenses
Monthly Housing Takeoff (PITI)
Amortization Balance & Cumulative Interest Decay Curve
Visualization tracking remaining principal balance over time (blue) versus cumulative interest accrued (red), highlighting the critical "amortization crossover point" and extra payment velocity.
Standard Fixed-Rate Amortization Formulas
Under federal banking standards, fixed-rate mortgage payments are derived using the actuarial annuity present-value formula. Monthly compounding calculates the exact periodic payment required to amortize principal $P_0$ to zero over $N$ months at periodic rate $r$:
M = P_0 \times \frac{r(1 + r)^N}{(1 + r)^N - 1}
\text{Where } r = \frac{\text{Annual Interest Rate}}{12}, \quad N = \text{Term Years} \times 12, \quad P_0 = \text{Purchase Price} - \text{Down Payment}
2. Monthly Escrow Components (PITI):
\text{Monthly Tax} = \frac{\text{Annual Property Tax}}{12}, \quad \text{Monthly Insurance} = \frac{\text{Annual Premium}}{12}
\text{Monthly PMI} = \begin{cases} \frac{P_0 \times 0.0075}{12} & \text{if } \text{Down Payment} < 20\% \\ 0 & \text{if } \text{Down Payment} \ge 20\% \end{cases}
3. Periodic Balance Recurrence:
I_k = B_{k-1} \times r \quad \text{(Interest Due)}, \qquad P_k = (M - I_k) + P_{\text{extra}} \quad \text{(Principal Paid)}
B_k = B_{k-1} - P_k \quad \text{(Ending Balance)}
5 Critical Mortgage Traps & Hidden Lending Pitfalls
1. The Year-Two Escrow Shortage Shock
Lenders calculate initial property tax escrow based on the previous homeowner's old tax assessment. In year two, county assessors reset taxable value to your actual new purchase price. The resulting tax increase creates an "escrow shortage," causing lenders to hike monthly payments by $300 to $600 to recoup past deficits.
2. Paying for Lender "Discount Points" You Never Recover
Lenders encourage borrowers to buy "discount points" (paying 1% of the loan amount upfront to lower the interest rate by 0.25%). On a $400,000 loan, 2 points cost $8,000 upfront to save ~$65/month. The break-even period is 10.2 years. If you refinance or sell within 7 years, you lose thousands.
3. FHA Loan MIP is Permanent (Unlike Conventional PMI)
On conventional loans, Private Mortgage Insurance (PMI) cancels automatically once equity reaches 20% to 22%. On FHA loans with less than 10% down, Mortgage Insurance Premium (MIP) remains for the entire 30-year life of the loan. The only way to eliminate FHA MIP is to refinance into a conventional mortgage.
4. The "Bi-Weekly Mortgage Payment" Fee Scam
Third-party companies charge $300 to $500 setup fees plus monthly maintenance to administer "bi-weekly payment plans." Paying 26 half-payments a year simply equals 13 full payments (one extra payment per year). You can achieve the exact same interest savings for free by adding 1/12th of your monthly payment to principal each month.
5. Miscalculating Early vs Late Prepayment Velocity
A $5,000 lump sum principal payment made in Year 2 saves over $22,000 in compounding interest over a 30-year loan because it eliminates 28 years of interest accrual on that capital. Making that same $5,000 payment in Year 26 saves less than $900 in interest. Early prepayment velocity is vastly superior to late payoff.