The Original Equation

Derivation of P(n) = P(0)e^rt

P(n) = Amount of mortgage left to pay

Li = Interest rate on loan

P(0) = Amount loaned

Pm(n) = Amount of income used to pay loan

n = Years

P(n) = enLi[P(0) - Pm(n)]
See the P(n) vs. Time graph
See the Raise Rate vs. Loan Interest graph