1. The cash prices of six-month and one-year Treasury bills are 95.0 and 92.0. A 1.5-year bond that will pay coupons of $4 every six months currently sells for $97.23. A two-year bond that will pay coupons of $5 every six months currently sells for $98.95. Calculate the six-month, one-year, 1.5-year, and two-year zero rates.
2. Suppose that 6-month, 12-month, 18-month, 24-month, and 30-month zero rates are 3%, 3.12%, 4.02%, 4.25%, and 4.32% per annum with continuous compounding respectively. Estimate the cash price of a bond with a face value of 100 that will mature in 30 months and pays a coupon of 4% per annum semiannually.