Calculate Macaulay’s duration, the modified duration, and the convexity of the following bonds (annualize the parameters). Assume all of the bonds pay principal at their maturity.

a. Four-year, 9% coupon bond with a principal of $1,000 and annual coupon payments trading at par.

b. Four-year zero-coupon bond with a principal of $1,000 and priced at $708.42 to yield 9%.

c. Five-year, 9% coupon bond with a principal of $1,000 and annual coupon payments trading at par.

d. 10-year, 7% coupon bond with a principal of $1,000 and semiannual coupon payments (3.5%) and priced at par.

e. Three-year, 7% coupon bond with a principal of $1,000 and semiannual coupon payments (3.5%) and priced at par.

f. Three-year zero-coupon bond with a principal of $1,000 and priced at

$816.30 to yield 7%.