Stuck on a "show that" question that is more interest rate related but I'll provide all the information needed below.
Given a consistent market, show that:
When $$A(0,t) = 1 + 0.05t, i_h(t)=\frac{(0.05)}{1+0.05t}$$ and that when $$A(0,t) = 1.05^t, i_h(t)=\frac{(1.05)^h-1}{h}$$
The definitions are listed below: $A(t,t+n)=1+h*i_h(t)$
A consistent market is one where $A(t_0,t_n)=A(t_0,t_1)*A(t_1,t_2)*...*A(t_{(n-1)},t_n)$
$i_h(t) = \frac{j}{h}$ where j is effective rate of interest for the period $(t,t+h)$
Please let me know if the question is unclear, as I have been struggling with this proof for a while now! I don't understand why for the first result $ i_h(t)=0.05$ is not correct.
I am also wondering how the first result is independent of $h$ and how the second result is independent of $t$.