Purpose and steps
Total monthly payment = principal and interest + home value × property-tax rate / 12 + annual insurance / 12 + HOA + loan amount × PMI rate / 12 when initial LTV exceeds 80%. The calculation runs locally and keeps cash-flow timing consistent with the stated assumptions.
- Confirm currency and monthly versus annual amounts. U.S. tax and loan models should be used within their stated scope.
- Prepare Home price, Down payment, Annual interest rate, Loan term, Annual property tax rate, Annual homeowners insurance, Monthly HOA dues, Annual PMI rate. Defaults demonstrate the model rather than your personal circumstances.
- Check the headline result and its components. A key interpretation for this tool is: PMI protects the lender; homeowners insurance protects the property. They are separate costs.
- Compare the baseline with a changed scenario: The 80% LTV date is an amortization estimate, not a promise of cancellation.
Input reference and units
These values reproduce the model’s demonstration. Replace them with your own records or measurements; they are not recommended targets.
On a small screen, swipe the table horizontally to see all columns.
| Parameter | Demonstration value | How to enter it |
|---|---|---|
| Home price | 400000 USD | Use dollars and the monthly or annual period stated in the field label; do not enter thousands of dollars. |
| Down payment | 20 % | Check the unit carefully: some tools use a percentage and others a cash amount. |
| Annual interest rate | 6.5 % | Enter a percentage such as 6.5, not 0.065. The equation converts it to a decimal. |
| Loan term | 30 years | Use years here. The model converts to months when the payment schedule requires it. |
| Annual property tax rate | 1.2 % | Enter a percentage such as 6.5, not 0.065. The equation converts it to a decimal. |
| Annual homeowners insurance | 1800 USD | Use dollars and the monthly or annual period stated in the field label; do not enter thousands of dollars. |
| Monthly HOA dues | 0 USD | Use dollars and the monthly or annual period stated in the field label; do not enter thousands of dollars. |
| Annual PMI rate | 0.5 % | Enter a percentage such as 6.5, not 0.065. The equation converts it to a decimal. |
Model-specific method
How this calculator produces its result
Total monthly payment = principal and interest + home value × property-tax rate / 12 + annual insurance / 12 + HOA + loan amount × PMI rate / 12 when initial LTV exceeds 80%.
Annuities and the remaining-balance recurrence
A fixed-payment loan is an annuity: the discounted value of all future payments equals the amount borrowed today. Summing that geometric series gives the monthly-payment equation. Match the rate and time unit: monthly payments use an annual nominal rate divided by twelve and a term counted in months.
Each payment is split into interest and principal. Interest uses the opening balance, so paying extra principal now reduces later interest. A zero rate must use P/n rather than the formula’s zero-over-zero form. Keep full precision during the schedule and round only for display; a lender may round each actual posting differently.
P = Σ[t=1…n] M/(1+r)^t M = Pr / (1 − (1+r)^−n) Iₜ = Bₜ₋₁r; Bₜ = Bₜ₋₁ + Iₜ − paymentₜ
- P: principal today
- r: rate per payment period, not the annual percentage
- n: number of payment periods
- M: scheduled payment; B: remaining balance
Worked example
A $400,000 home with 10% down has a $360,000 loan. At a 0.5% PMI rate, initial PMI is $150 a month; 1.2% property tax adds $400 and $1,800 annual insurance adds $150.
Reproduce the default scenario
This is a separate example, calculated using the exact engine on the tool page and the defaults in the input reference above. Health examples use metric units. Displayed rounding may differ from intermediate precision.
- Initial total monthly housing payment
- 2,572.62 USD
- Principal and interest
- 2,022.62 USD
- Property tax
- 400 USD
- Homeowners insurance
- 150 USD
- PMI
- 0 USD
- HOA dues
- 0 USD
- Loan amount
- 320,000 USD
- Down payment
- 80,000 USD
- Loan-to-value
- 80%
- Total loan interest
- 408,142.36 USD
- Estimated months to 80% LTV
- 0 months
- PMI until estimated 80% LTV
- 0 USD
Reading results without overstating them
- PMI protects the lender; homeowners insurance protects the property. They are separate costs.
- The 80% LTV date is an amortization estimate, not a promise of cancellation.
Assumptions and exclusions
- Models conventional fixed-rate loans with a flat PMI premium until estimated 80% original-value LTV. Requested cancellation at 80% and automatic termination at 78% have conditions; FHA, VA, escrow changes and refinance are not modeled.
Sources and content notes
Toolify describes the implemented algorithm and its assumptions. Sources below support the topic or applicable rules; they do not endorse this calculator. Examples are illustrative, and published rules take precedence over simplified estimates.
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