Question

Jayce is borrowing $148,000 to buy a house. He is taking out a 30 year mortgage with a 5.35% fixed interest rate. Property taxes are $4,975 and homeowners insurance is $1125 per year. PMI is $75 per month. Find his total monthly (PITI) payment. Show your work.

Answer 1

The formula used to calculate the fixed monthly payment ($ P) required to fully amortize a loan of $ L over a term of n months at a monthly interest rate of r is

P = L[r(1 + r)ⁿ]/[(1 + r)ⁿ - 1].

Here, L = 148000, r = 5.35/1200 ( assuming monthly compounding as payments are being made monthly) and n = 30*12 = 360.

Hence P = 148000*(5.35/1200)*[ (1+5.35/1200)³⁶⁰ ] / [ (1+5.35/1200)³⁶⁰ -1] =148000*(5.35/1200)*4.960134141/ 3.960134141 = $ 826.45.

The property taxes are $ 4,975 and homeowners insurance is $1125 per year i.e. $ 414.58 and $ 93.75 per month.

Therefore, the total monthly payment is $ (826.45+414.58+93.75+75) = $ 1409.78 ( on rounding off to the nearest cent).