Third year principal reductionPMT - [P - A - A(1+r)]r=(PMT-P r)+Ar + A(1+r)r=A+Ar+Ar+Ar^2=A*(1+r)^2 You make it A + Ar + Ar^2. Hence wrong answer. When cakculating the interest payment, the principal reduction in all previous years accumulate. Too complicated for you and there is fixed answer in mathematics. Switch to continue to argue in the topic without fixed answer.