The Amortization Formula Every Developer Should Know

I have built loan calculators for three different fintech products. Each time, the product team assumed the monthly payment calculation was straightforward. Each time, edge cases in the amortization formula caused bugs that took days to trace. Here is the math, the implementation, and the traps. The standard amortization formula The fixed monthly payment for a fully amortizing loan: M = P * [r(1+r)^n] / [(1+r)^n - 1] Where: M = monthly payment P = principal (loan amount) r = monthly interest rate (annual rate / 12) n = total number of payments In JavaScript: function monthlyPayment ( principal , annualRate , years ) { const r = annualRate / 100 / 12 ; const n = years * 12 ; if ( r === 0 ) return principal / n ; return principal * ( r * Math . pow ( 1 + r , n )) / ( Math . pow ( 1 + r , n ) - 1 ); } // $250,000 loan at 6.5% for 30 years monthlyPayment ( 250000 , 6.5 , 30 ); // $1,580.17 That zero-rate check on line 4 is not theoretical. Promotional 0% financing exists, and without that