Hello. I am wondering about a specific mortgage formula.

The formula I found:

P = monthly payment

L = principal

c = monthly interest

n = total months of amortization

Thus:

P = L[c(1+c)^n]/(1+c)^n-1

Question: Is this the proper formula? Why is it the proper formula?

I can use the formula, but I do not understand it. I want to get to the point where I can explain how the formula is derived in english.

The numerator: L[c(1+c)^n]

This is trying find the 'money' that is being paid. The term (1+c)^n gives you the total interest that you pay over the life of the loan.

Since we are trying to find the monthly payment, we don't care about that. So, we take the total interest that is paid over the life of the loan, and scale it from the life of the loan to a monthly interest payment, hence c(1+c)^n .

The denominator: (1+c)^n-1

This is where I get confused. In the numerator, we found the real interest rate. In the denominator, what are we trying to find?