To calculate the monthly payment for a standard fixed-rate mortgage, we use the :
The fundamental principle of any mortgage is that a dollar today is worth more than a dollar tomorrow due to its potential earning capacity. When a lender provides a lump sum (the principal) to a borrower, they are essentially "selling" the use of that money. The price of this service is the interest. mortgage mathematics
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 To calculate the monthly payment for a standard
, typically tied to an index (like the SOFR) plus a margin. This introduces a "re-casting" element where the monthly payment is recalculated at specific intervals, potentially changing the borrower’s financial obligations overnight. Conclusion Mortgage mathematics is the study of the financial
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