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FHA Loan Formula and Mortgage Insurance Calculation

Learn the FHA base loan, monthly payment, amortization, upfront MIP, annual MIP, ownership-cost, cash-to-close, and loan-limit formulas.

How do the FHA Loan Calculator formulas work?

This formula page defines the variables used by the FHA Loan Calculator, shows how those values are combined, and explains the order of operations behind the result. Use the worked steps to verify an estimate, compare scenarios, and understand which assumptions or rounding rules can affect the displayed answer.

Formula Overview

The FHA calculator follows four connected calculations. It derives the base loan and upfront mortgage insurance, calculates the fixed payment on the financed balance, selects the annual MIP rate and duration, and adds property costs to the initial monthly estimate.

The local loan-limit check uses the base loan, not the balance after financed upfront MIP. Annual mortgage insurance is estimated from the original amortization schedule using HUD's average-outstanding-balance procedure.

Variable Definitions

SymbolMeaningUnit or convention
VEntered purchase price used as the value proxyCurrency
DCash down paymentCurrency
BBase loan amountV - D
UUpfront mortgage insurance premium1.75% of B
PFinanced balance used for principal and interestB + U when U is financed; otherwise B
iMonthly note rateAnnual rate / 1,200
nScheduled monthly paymentsTerm years x 12
MMonthly principal-and-interest paymentCurrency per month
LTVOriginal loan-to-value used by the modelB / V
qAnnual MIP rate selected by ruleDecimal
A(y,m)Outstanding financed balance in year y, month mCurrency
FEntered local FHA loan limitCurrency

Monthly Payment

The base loan and upfront MIP are:

B=V−DB=V-D
U=0.0175BU=0.0175B
P={B+U,UFMIP financedB,UFMIP paid in cashP=\begin{cases}B+U,&\text{UFMIP financed}\\B,&\text{UFMIP paid in cash}\end{cases}

The fixed monthly principal-and-interest payment is:

M=Pi1−(1+i)−nM=P\frac{i}{1-(1+i)^{-n}}

When the entered note rate is zero, the engine uses M = P / n. The initial total payment adds monthly MIP and entered ownership costs.

Amortization

For each month, the schedule separates interest and principal:

Interestm=Balancem−1×iInterest_m=Balance_{m-1}\times i
Principalm=M−InterestmPrincipal_m=M-Interest_m
Balancem=Balancem−1−PrincipalmBalance_m=Balance_{m-1}-Principal_m

The final payment clears any remaining cent difference. Annual rows add the monthly principal and interest and report the year-end balance.

HUD periodic MIP method

Aˉy=112∑m=112A(y,m)\bar{A}_y=\frac{1}{12}\sum_{m=1}^{12}A(y,m)
Premiumy=round⁡(Aˉyq,2)Premium_y=\operatorname{round}(\bar{A}_y q,2)
Premiumy∗=round⁡(Premiumy1+0.0175,2)Premium_y^{*}=\operatorname{round}\left(\frac{Premium_y}{1+0.0175},2\right)
MIPmonth,y=round⁡(Premiumy∗12,2)MIP_{month,y}=\operatorname{round}\left(\frac{Premium_y^{*}}{12},2\right)

The starred step applies when upfront MIP is financed. The calculator limits assessed months to the rate rule's 11-year period or mortgage term.

Extra Payments

The engine does not include extra principal in the FHA amortization or periodic-MIP schedule. It uses the original scheduled payment and original amortization balance for the educational estimate.

To model voluntary principal payments, transfer the financed balance, note rate and term to the Extra Payment Calculator. Do not assume the projected early payoff changes FHA MIP treatment without confirmation from the servicer or lender.

Ownership Costs

The initial total monthly estimate is:

Paymentinitial=M+MIPmonth,1+Taxannual12+Insuranceannual12+HOAmonthPayment_{initial}=M+MIP_{month,1}+\frac{Tax_{annual}}{12}+\frac{Insurance_{annual}}{12}+HOA_{month}

Estimated cash to close is:

Cashclose=D+Closing+{0,UFMIP financedU,UFMIP paid in cashCash_{close}=D+Closing+\begin{cases}0,&\text{UFMIP financed}\\U,&\text{UFMIP paid in cash}\end{cases}

The local limit status is based on B less than or equal to F. The remaining amount is F - B; a negative result means the base loan exceeds the entered limit.

Annual MIP rate and duration

Term and base loanOriginal LTVAnnual MIPModeled duration
Over 15 years, at or below $726,200At or below 90%0.50%11 years
Over 15 years, at or below $726,200Over 90% through 95%0.50%Term
Over 15 years, at or below $726,200Over 95%0.55%Term
Over 15 years, above $726,200At or below 95% / over 95%0.70% / 0.75%11 years only at or below 90%; otherwise term
15 years or less, at or below $726,200At or below 90% / over 90%0.15% / 0.40%11 years / term
15 years or less, above $726,200At or below 78% / over 78% through 90% / over 90%0.15% / 0.40% / 0.65%11 years / 11 years / term

Worked Calculation

Use a $400,000 purchase, $14,000 down, financed upfront MIP, 6.25% fixed rate and 30-year term.

  1. Base loan: $400,000 - $14,000 = $386,000.00.
  2. Upfront MIP: $386,000 x 0.0175 = $6,755.00.
  3. Financed balance: $386,000 + $6,755 = $392,755.00.
  4. Monthly rate: 0.0625 / 12 = 0.00520833.
  5. Scheduled payments: 30 x 12 = 360.
  6. Principal and interest: $2,418.26 per month.
  7. Original LTV: $386,000 / $400,000 = 96.50%.
  8. The modeled annual MIP rate is 0.55% for the mortgage term.
  9. With $400 monthly tax, $150 insurance and no HOA, the initial total is approximately $3,144.24.

Assumptions

  • The mortgage is a standard fixed-rate FHA Title II forward purchase loan.
  • The entered purchase price is the value proxy; actual maximum-mortgage calculations use the applicable adjusted value.
  • The annual MIP schedule is the standard forward-mortgage schedule cited from HUD Mortgagee Letter 2023-05.
  • The local loan limit is supplied by the user and must match county or metropolitan area, units and case-number year.
  • Property tax, homeowners insurance, HOA dues and other entered costs remain constant.
  • Special programs, legacy refinance exceptions, lender overlays, points, credits, prepaids, reserves and underwriting are excluded.
  • Money is displayed to cents. Upfront MIP is truncated to cents following the modeled HUD instruction, while periodic MIP follows the stated cent-rounding sequence.

Formula FAQ

Why is the financed loan larger than the base loan?

Financing upfront MIP adds the premium to the balance used for principal and interest. The base loan remains the amount used for the local-limit and MIP-rule checks. Review the FHA Loan Calculator formula assumptions before relying on this result for decisions.

Why can monthly FHA MIP decline?

The periodic premium is based on the annual average outstanding balance from the original amortization schedule. That balance generally declines as principal is repaid. Use realistic inputs and review the FHA Loan Calculator formula assumptions before relying on this result for decisions.

Why does a 10% down scenario show 11 years of MIP?

Under the cited standard schedule, an original LTV at or below 90% generally receives an 11-year annual-MIP duration. Program and case details still require lender review. Review the FHA Loan Calculator formula assumptions before relying on this result for decisions.

Does the formula determine eligibility?

No. Eligibility depends on borrower, property, appraisal, occupancy, credit, income, debt, assets and program requirements outside this calculation. For a useful FHA Loan Calculator formula result, use realistic inputs, compare relevant scenarios, and review the stated assumptions before making a decision.

References

Use the FHA Loan Calculator