Consider a 30 year, 4% semiannual coupon bond currently selling at par ($1000). Compute the following as accurately as possible, and report your answers to four decimal places:

(i) price value of a basis point 1

(ii) modified duration, using

a) the formula

b) the numerical approximation with a 1 basis point change in yield

c) the numerical approximation with a 50 basis point change in yield

(iii) convexity measure, using

a) the numerical approximation with a 1 basis point change in yield

b) the numerical approximation with a 50 basis point change in yield