Suppose you are interested in obtaining a mortgage loan for $250,000 in order to purchase your principal residence. Your lender has suggested that you might be interested in taking an FHA loan. In order to do so, you must pay an additional up-front mortgage insurance premium (UFMIP) of 1.0% of the mortgage balance. If the interest rate on the fully amortizing mortgage loan is 5% and the term is 30 years, what is your monthly mortgage payment assuming the UFMIP is financed

if you are going to finance the up-front mortgage insurance premium, then the total principal of the loan will increase by 1%, so it will be = $250,000 x 1.01 = $252,500. It is normal to finance UFMIP payments since they are additional closing costs and the whole purpose of FHA loans is to allow more people to be able to buy a house.

we can use the present value of an annuity formula to determine the monthly payment.

monthly payment = principal / PV annuity factor

principal = $252,500
PV annuity factor = 186.2816

monthly payment = $252,500 / 186.2816 = $1,355.474722 ≈ $1,355.47

I prepared an amortization schedule in order to check the answer. At the end the final balance is $3.83, but that is because you have to round to the nearest cent. If the payment is rounded to $1,355.48, the the balance is -$4.50.