A rainbow is a cash-flow stream which pays $1 at time 1 and 2n; $2 at time 2 and 2n – 1; ...;$(n-1) at time n - 1 and n + 2; and $n at time n and n + 1 and $n at time n for n > 1. 

(a) With the use of a time diagram, argue that the current value at time n of a rainbow is sna¨n.

(b) By using the formula x + y ≥ 2 √xy for x, y ≥ 0, show that vk + (1 + i)k ≥ 2 for any positive integer k.

(c) Hence or otherwise, show that sna¨n ≥ n2. When does the equality hold? What is the significance of this result?