Using the same no-arbitrage argument to derive Formula 4.3

(a) Provide an expression for the forward exchange rate, \(F_{X}(0, T)\), for any \(T\) using simple (add-on) domestic and foreign interest rates, \(r_{d}, r_{f}\).

(b) Using the Taylor Series approximation \((1+x)^{\alpha} \approx 1+\alpha x\) and ignoring terms of \(T^{2}\) and higher, which is justified for small \(T\), say \(T<0.5\),

provide an approximate formula for the forward exchange rate in terms of spot exchange rate, \(X(0)\), and simple (add-on) interest rate differential \(r_{f}-r_{d}\).

(c) Derive an expression for \(F_{X}(0, T)\) using continuously compounded \(r_{d}, r_{f}\), and use the Taylor Series approximation \(e^{x} \approx 1+x\) and ignoring terms of \(T^{2}\) and higher, provide an approximate formula for \(F_{X}(0, T)\) in terms of \(X(0)\) and \(r_{f}-r_{d}\).