Consider a zero-coupon bond with face value $10, 000 and maturity 10 years. Assume that r(10) = 4.8736%.

(a) Compute the convexity of the bond.

(b) Compute the exact price change in the bond corresponding to a 35 bp increase in r(10).

(c) Compute the first-order approximation to the price change in the bond for a 35 bp increase in r(10).

(d) Compute the second-order approximation to the price change in the bond for a 35 bp increase in r(10).