Futures = forward, general deterministic rates

Let the short rate $r(t)$ be a deterministic function, and futures be settled at $t_0 < t_1 < \dots < t_n = T$. (a) Write the proof of Prop. 7.5 in full for this case, defining the holdings $\delta_i$ explicitly and verifying that the strategy is self-financing once the variation margin is invested or borrowed at the risk-free rate. (b) For constant $r$, show the number of contracts held on the first day is $e^{-r(T - t_1)}$ and the number on the last day is 1. (c) Identify the exact step that fails when $r$ is stochastic.