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What is the formula for monthly payment of mortgage including Term, Interest Rate, Cost of Home Down, Payment Insurance, Property Tax, HOA Fee. I'm a programmer and want to add this functionality to my site. The following is a basic formula is found out by googling.

Number of Months, n = [Term (in number of years, not months)*12]
Monthly Interest rate, c = [Interest Rate(Yearly)/12]
Loan Amount, L = [Cost of Home] - [Down Payment]
Monthly Payment, P = L[c(1 + c)^n]/[(1 + c)^n - 1]
Additional Monthly Expenses, E= [Insurance (annual)/12] + [Property Tax (annual)/12] + [HOA Fee (monthly)]
Total Monthly Payment, TMP = P + E

But this doesn't seem to be accurate. can someone help me on this?

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