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If you have ever gotten a mortgage, you have probably wondered just how exactly the monthly payment is determined, and what the formula is for it. It is a common misconception among those new to financing that the formula for deriving these calculations is a simple matter of identifying a percentage of the loan, and charging it, in addition to the monthly fraction of the principal, to the borrower. While this is the most intuitive way of understanding amortization, it is thankfully incorrect, as we would all be paying quite a lot more than we actually do if it were true!
The actual formula, which will look a bit more confusing, looks something like this. In this equation, P is the principal amount borrowed, A the periodic investment, and n is the total number of monthly payments (in the case of a conventional 30 year mortgage, this would be 360), and r is the interest rate. A more detailed explanation of the detail of the formula can be found here.
The reason for the complexity is a matter of banking profit; because it is more likely that a loan will be paid off in full sooner rather than later, it makes logical sense to prioritize high amounts of interest at the start of the loan term. This allows banks to maximize profit while being able to loan at highly competitive interest rates; the amortization equation is simply the equilibrium point of many centuries’ worth of competitive lending, so as to maximize benefit to the customers and the bank.
However, it does nonetheless provide a bit of confusion to those who are trying to figure it out intuitively, so to them I would recommend, simply make use of business loan calculators. It’s a lot easier, and you will be a lot happier that way.