Answer:
To find the amount of interest in Ellen's 133rd payment, we need to determine the monthly payment amount and calculate the principal portion for that payment.
Since Ellen has a thirty-year mortgage with level monthly payments, we can assume she has made consistent payments throughout the mortgage term. Therefore, the principal portion of her 82nd payment should be equal to the principal portion of her 56th payment.
Let's denote the monthly payment amount as P. We can set up the following equation based on the given information:
82nd payment: Principal + Interest = $246.31
56th payment: Principal + Interest = $220.14
Since the interest portion of each payment remains the same, we subtract these two equations to eliminate the interest variable:
82nd payment - 56th payment: Principal + Interest - (Principal + Interest) = $246.31 - $220.14
Simplifying the equation:
Principal - Principal + Interest - Interest = $26.17
0 = $26.17
This equation tells us that the principal portion cancels out, and the interest portion is zero. This means that Ellen has fully paid off her mortgage by her 82nd payment.
Therefore, in her 133rd payment, the interest portion would also be zero.