20. A bank has made the promise that for some fixed i > 0, an investment with it will grow over every one-year period as Fjþ1 ¼ Fjð1 þ iÞ, where Fj denotes the fund at time j in years. Develop a proof by contradiction in the form of (1.9) that for any nb1, Fn ¼ F0ð1 þ iÞn:
(Hint: Define A : Fjþ1 ¼ Fjð1 þ iÞ for all jb0; C : Fn ¼ F0ð1 þ iÞn for all nb1. If A5@C and N is the smallest n that fails in C, what can you conclude about FN, which provides a contradiction, and about the conclusion A ) C?)