FHA Payment Calculator with MIP

An FHA-style monthly payment is four separate calculations added together, usually written PITI + MIP:

1. Principal and interest on the loan amount
2. Mortgage insurance premium (MIP), charged monthly
3. Property taxes, one twelfth of the annual bill
4. Homeowners insurance, again one twelfth

The loan itself is built in two steps. The base loan is

$L_{\text{base}} = \text{price} - \text{down payment}$

and the upfront MIP, at rate $u$, is normally financed rather than paid in cash, so the amount actually amortized is

$L = L_{\text{base}} (1 + u)$

Important: the upfront rate $u$, the annual MIP rate $a$, the minimum down payment, loan limits and how long MIP lasts are all programme rules set by the FHA and by lenders. They change, and they depend on your loan-to-value ratio and term. AI-Math publishes none of them and is not a lender — look up the figures that apply to your loan and enter them here; the page shows the arithmetic.

Loan-to-value

$\text{LTV} = \frac{L_{\text{base}}}{\text{price}}$

LTV drives the annual MIP rate and, on many programmes, how long the premium is charged. It is computed on the base loan against price (or appraised value, whichever the lender uses), not on the loan after upfront MIP is rolled in.

Principal and interest

$M = L \cdot \frac{r(1+r)^n}{(1+r)^n - 1}$

with $r$ the monthly rate and $n$ the number of payments. Note that $L$ here includes the financed upfront MIP, so you pay interest on it for the life of the loan.

Monthly MIP

$\text{MIP}_{\text{monthly}} = \frac{L \times a}{12}$

where $a$ is the annual MIP rate as a decimal. Lenders typically recompute it each year from the average outstanding balance, so the figure drifts down slowly rather than staying fixed.

Total

$\text{Payment} = M + \text{MIP}_{\text{monthly}} + \frac{\text{annual tax}}{12} + \frac{\text{annual insurance}}{12}$

Add HOA dues separately if they apply — they are not part of PITI.

• Amortizing the base loan and then adding MIP separately: if the upfront premium is financed, it is part of the balance. Compute $L = L_{\text{base}}(1+u)$ first, then run the payment formula.
• Applying the upfront rate to the purchase price: $u$ applies to the base loan, after the down payment comes out.
• Calling FHA mortgage insurance "PMI": PMI is the private insurance on conventional loans; FHA charges MIP under different rules. People search for both, but the cancellation terms are not the same.
• Assuming MIP falls off automatically: whether and when it ends depends on the programme terms in force for your loan. That is a rules question, not an arithmetic one.
• Using stale rates: any $u$ and $a$ you find in an article may already be out of date. Take them from current official sources.
• Quoting P&I as "the payment": taxes and insurance are often a large share of the monthly total.
• Forgetting the annual rate divisions: $r = \text{APR}/12$ and $a$ is divided by 12 too.