Government-backed mortgage insurance, at a mechanical level

Some programs collect an insurance premium up front and permit that premium to be added to the loan. The house's cash price does not move. The balance does. Track 1 lesson 3 is a larger loan on unchanged value: market value stays put, the amount counted against it rises. Financing a premium is that rise, done by wrapping a fee into P. Rules vary by program. This lesson is the arithmetic of one invented book, not a map of any program.

Ilex Lending prices a house at $268,500. A 3.5 percent down payment is $9,382.50. Base loan is $268,500 − $9,382.50 = $259,117.50. Upfront insurance is 1.75 percent of the base: $259,117.50 × 0.0175 = $4,534.56, financed. Total loan is $259,117.50 + $4,534.56 = $263,652.06. Annual insurance is 0.55 percent of the base: $259,117.50 × 0.0055 = $1,425.15 a year, $118.76 a month.

Day-one LTV on the cash price, including the financed upfront, is $263,652.06 ÷ $268,500 = 98.2 percent. The $4,534.56 did not buy more house. It bought the same house with a larger numerator. Lesson 14's conventional charge sat on top of P as a monthly fee. This upfront charge sat inside P as extra principal, and a smaller annual charge still sits on top of the base.

Two wrappers, one geometry. A fee outside the loan leaves P still and adds a line to the payment. A fee inside the loan raises P and then accrues interest on that raise for the term. Track 1 lesson 3 already named the second object: more loan, same collateral. Program rules on who pays what, for how long, and on what base, vary. A reader's own situation belongs with a qualified professional.

Financing a premium is a larger loan on an unchanged cash price. The 98.2 percent LTV is the house plus the fee, divided by the house.