2 (a) An aircraft lease ending in 2 years has two remaining payments of $10 million due on it (payments are due in exactly one and two years time respectively). The appropriate discount rate, r0, is 3%. Express the present value of the pay ments in terms of the interest rate r0 as a function: f (r0).

(i.) Use the Taylor series expansion to the first order to approximate the present value of the lease payments if interest rates change to r = 5%. (ii.) Compare this to the actual value calculated using the original function, f(r). How might the accuracy of the approximation be improved?