ALL following bonds have semi annual coupon rates

You have information on the following on-the-run Treasury securities: 6-month T-bill, price = $95.694 per $100 par value; 1-year T-bill, price = 92.902 per $100 par value. Also, information on the following off-the-run Treasury securities: T-note, CR = 6%, F = $100,000, maturity = 18 months, price = 98-243;

T-bond, CR = 7%, F = $100,000, maturity = 2 years, price = 101-12+. a) Show that the spot rates are as follows: z1 = 4.50%, z2 = 3.75%, z3 = 3.42%, z4 = 3.09%

b) Show that the implied forward rates are as follows: f1 = 3.01%, f2 = 2.76%, f3 = 2.11%.

c) Show that if a forward contract is to deliver a 1.5-year T-note with F = $100 and CR = 4%, to be delivered in half year (i.e. 1 period from now), the delivery price should be $98.20