You are given the following bond price data (each bond has a face value of $100):

A 26-week zero coupon bond has a price of $99.20

A 13-week bond that pays coupons quarterly at a rate of 3% per annum has a price of $100.5485

A 39-week bond that pays coupons quarterly at a rate of 6% per annum has a price of $103.1655

A 52-week bond that pays coupons semi-annually at a rate of 5% per annum has a price of $103.0325

(a) Calculate the discount factors, Z(0; T), for T=13 weeks, 26 weeks, 39 weeks and 52 weeks.

(b) Assuming continuous compounding of interest, characterize the term structure of interest rates generated by these bond prices.

(c) Hence calculate the value of a 52-week bond that has a face value of $500 and pays coupons quarterly at a rate of 10% per annum.

(d) What is the yield to maturity of this bond?