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Financial Mortgage amortization Question. How to manually calculate?

I'm a smart guy and used to know how to do this.

I undergrad'ed in finance, but Mastered in Physics. The finance formulas were uber-easy, but I can't remember how to know how much principle to pay down the on the first payment so that


my style of calculating mortg is to use engineering method of calculation using financial language. i am not good in using logic.
m1=1 annual compounded
m1=2 semi-annual compounded
m1=4 quarterly compounded
m1=12 monthly compounded

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Calculating mortgage payments for a home requires information on interest rates, amortization and the loan amount. Calculate monthly mortgage ...