Having heard of your knowledge of present value techniques, you have been asked to

testify as an expert witness in the following lawsuit.

Several homeowners in a nearby community have organized to protest against alleged

gouging on the part of a local lending institution. One resident presents his payment book

as evidence.

The resident has a $30-$year, fixed rate loan at $6$ percent interest for $$200,000.$ He got the

loan $10$ years ago and has been making equal annual payments of $$14,529\mathrm{.}60$ ever since.

He observes that he has paid the lending company $$145,296\mathrm{.}00$ yet his payment book

indicates that the principal due on the loan has only declined by $$33,345\mathrm{.}40.$ He presents

this as obvious proof of "gouging on the part of the money changers".

Required:

Do you agree? Why, why not? $($Support your answer with any relevant calculations.$)$