Mortgage Mathematics ◎

Furthermore, the "math" of mortgages allows for strategic acceleration. By making one extra payment per year—or paying bi-weekly instead of monthly—a borrower can significantly alter the amortization schedule. Because interest is calculated on the remaining balance, any early reduction in principal prevents that specific amount of money from ever accruing interest again, effectively shortening the loan term and reducing the total interest paid. 4. Adjustments and Variables

Mortgage mathematics is the study of the financial mechanics behind long-term property financing. While a mortgage may appear to be a simple loan, it is governed by the principles of , time value of money (TVM) , and compound interest . At its core, mortgage math seeks to determine how a fixed monthly payment can simultaneously pay down interest and reduce the principal balance over a set horizon. 1. The Foundation: Time Value of Money mortgage mathematics

M=Pr(1+r)n(1+r)n−1cap M equals cap P the fraction with numerator r open paren 1 plus r close paren to the n-th power and denominator open paren 1 plus r close paren to the n-th power minus 1 end-fraction = Total monthly payment P = Principal loan amount r = Monthly interest rate (annual rate divided by 12) n = Total number of payments (months) 2. The Amortization Process Furthermore, the "math" of mortgages allows for strategic