How could you compute for the monthly loan payments manually without using those loan calculators?

Answer 1

Let
r = annual interest rate
r/12 = monthly rate (this is the way mortgates work)
y = term of loan in years
A = amount of loan
P = monthly payment

P = A / [{1 - [1/(1 + r/12)]^(12y)} / (r/12)]

Answer 2

I already answered this question.

The annual payment over n years,

A =
P / [1/(1+r) + 1/(1+r)^2 + 1/(1+r)^3 + ... 1/(1+r)^n ]