## A not so intuive amortization problem

A loan at ${j_1} = 9\%$ is being repaid by monthly payments of $750 each. The total principal repaid in the 12 monthly installments of the 8th year is$400. What is the total interest paid in the 12 installments of the 10th year?

The answer is of course \$8,524.76
The answer makes use of the fact that the entries in the principal repaid column (especially in a no rounding scenario) are in the ratio of 1 + i.
An interesting question of course is whether it's possible to solve for the amount of the loan and loan term from the given information.
Apparently, it is.