The price of a risky 8-year zero-coupon bond depends on two parameters: risk-free 8-year spot rate (8) (to simplify notations, denote (8) by r), and the risk factor s and it is given by

(, ) = $1,000,000 . (1+0.5+32)16

Assume that today r=0.07 and s=0.4, so, todays bond price is (0.07,0.4) = $1,000,000 = $345,905.35.

(1+0.50.07+30.070.4^2)16

You want to estimate the change in the bonds price using the first-order Taylor series approximation, i.e., write the change in price P as a linear function of the change in the interest rate r and the risk factor s as P=A*r+B*s, where A and B are some constants.

a) (5 points) Find A and B. Round your answer to the nearest integer number. b) (2 points) Using the original price function, (, ) = $1,000,000 , if the risk factor increases by 0.05 (i.e., from 0.4 to 0.45), by how much the interest rate should change to keep the price unchanged?

c) (2 points) Using the Taylor series approximation, if the risk factor increases by 0.05 (i.e., from 0.4 to 0.45), by how much the interest rate should change to keep the price unchanged?