Problem 1.2 During the lecture the forward instantaneous rate f(T) was introduced, as the forward rate for the period (T, T +dT). This is given in terms of the zero rate R(T) by (2) f(T) = R(T) +TR'(T) Assuming that f(T) is known, derive the zero rate R(T). Show that the zero rate R(T) can be interpreted as the average of the forward instantaneous rate f(t) over t e [0, T]. Hints: Divide the time interval [0, T) into n equal intervals of length T=T, and assume simple compounding over each interval. n Problem 1.2 During the lecture the forward instantaneous rate f(T) was introduced, as the forward rate for the period (T, T +dT). This is given in terms of the zero rate R(T) by (2) f(T) = R(T) +TR'(T) Assuming that f(T) is known, derive the zero rate R(T). Show that the zero rate R(T) can be interpreted as the average of the forward instantaneous rate f(t) over t e [0, T]. Hints: Divide the time interval [0, T) into n equal intervals of length T=T, and assume simple compounding over each interval. n