Mortgage Division: Often a mortgage payment stream is divided into a principal payment stream and an interest payment stream and the two streams are sold sepa- rately. Consider a standard mortgage of initial value M = M(0) with equal periodic payments made of amount B. If the interest rate used is r per period, then the mort- gage principal after the kth payment is made satisfies M(K) = (1+r)M(K - 1) - B | for k = 0,1,.... This equation has solution M(K) = (1+r)* M = ((1+r)* B. Suppose that the mortgage has n periods and B is chosen so that M(n) = 0, so (1) B = r(1+r)"M (1+r)" -1 The kth payment has an interest component of I(k) = rM(k-1) and a principal payment of P(k) BrM(k-1) = (2) a) Find the present value, V, if the principal payment stream in terms of B,r,n, M. b) Find V in terms of r, n, M only. c) What is the present value, W, of the interest payment stream? d) What is the value of V as time approaches infinity (i.e. n ). d) Which stream do you think has the larger duration - principal or interest?