An aircraft lease ending in 3 years has three remaining payments of $10 million due on it (payments are due in exactly one, two, and three years time respectively). The appropriate discount rate, r0, is 4%. Express the present value of the payments in terms of the interest rate r0 as a function: f (r0).

(a) (10 pts) Use the Taylor series expansion to the first order to approximate the present value of the lease payments if interest rates change to r = 6%.

(b) (5 pts) Compare this to the actual value calculated using the original function, f (r). How might the accuracy of the approximation be improved?