The Loan Formula Your Bank Doesn't Want You to Know

Most loan calculators give you a number. This one shows you the math behind it — and why the difference between a 15-year and 30-year mortgage is more dramatic than most people realize. What a loan calculator actually does When you enter a loan amount, interest rate, and term into a loan calculator, it's solving a version of this formula: M = P × [r(1+r)^n] / [(1+r)^n − 1] Where: M = monthly payment P = principal (amount borrowed) r = monthly interest rate (annual rate ÷ 12) n = total number of payments (term in years × 12) Most people stop there. The interesting part is what happens when you start adjusting variables. Why a 15-year mortgage costs less than it looks Take a $300,000 mortgage at 6.5%: 30-year term : $1,896/month, total cost: $682,000 15-year term : $2,586/month, total cost: $465,000 The 15-year costs $690 more per month. But over the life of the loan, you save $217,000 in interest. That's a 36% reduction in total interest paid. The reason is compounding in reverse — you'