l'll'llMUU: UUN'I'IDI UU U :5 'l'IMJEi 1'11\" AN U15 First Semester Examinations June, 2021 Question 1. You live in a countryr where interest rates Ina].r be positive, zero or negative. A negative interest rate means a borrower is credited (rather than charged) interest on a loan, while an investor is charged (does not gain} interest on a deposit. As usual, denote the continuoust oompounded interest rate [whether positive, zero, or negative) by r. (a) In no more than a paragraph, explain in general terms the circum- stanoas that might give rise to a negative interest rate, and the intentions of the central bank in adopting it. [2 marks] {b} As you know, the holder of a forward oontraet agrees to deliver or take deliver].P at time T of an asset (St) for a price Fa agreed on at time 0. Suppose r a: ll. Which of the following is correct: [i] E] = Sue'T; or (ii) Fa = Sne'lrlT; or (iii) E; = Soc'1". [1 mark] (e) Give a rigorous proof, using principles we adopt in the course, of your choice in Part (b). State the principle[s) you use. [Ill marks] (d) Suppose r 3:1 0. Width of the following is oorreet? Give reasons. (i) F0 = SuErT; or (ll) Pa = SuIr\"; 01' (ill) Fa = Sufr. [1 mark]