[Loosely based on a problem in the notes of Emily Moore.]
The new president of Grinnell has decided that Grinnell should keep a supply of Zoomsters on campus so that students, staff, and faculty can more easily get around campus. Experience shows that Zoomsters last for ten years and then fall apart, at which point the pieces are worth $100. Acme also sells Zoomcoat, which they claim gives the Zoomster a lifespan of five more years. However, Zoomcoat-treated bikes have no scrap value.
Acme has signed a contract committing to sell us Zoomsters for $1,100 and Zoomcoat for $300 for the foreseeable future. If Grinnell makes 5% interest on the endowment, should it purchase Zoomcoat?
If you ignore the interest, the problem should be much easier. You may want to try the easier problem first.
Is this problem similar to any other problem we've encountered? If so, which one(s) and how?