Assume that the six-month Treasury spot rate is 1.6% APR, and the one-year rate is 2% APR, both compounded semiannually. What is the price of a one-year $1000 par Treasury bond with 2% coupons

Explanation:

Coupon rate = 2%, Par value = $1000

Treasury bond pays coupon semi annually

Coupon payment = (Coupon rate * par value) / 2 = (2% x 1000) / 2 = 20 / 2 = $10

Cash flow in six months = Coupon payment = $10

Cash flow in 1 year = Coupon + par value = 10 + 1000 = 1010

Discount rate for cash flow in 6 months = six-month Treasury spot rate i= 1.6% APR

Semi annual discount rate for cash flow in 6 months = 1.6% / 2 = 0.8%

Discount rate for cash flow in 1 year = 1 year Treasury spot rate i= 2% APR

Semi annual discount rate for cash flow in 1 year = 2% / 2 = 1%

Price of Treasury bond = present value of cash flow in six months discounted at semi annual discount rate + Present value of cash flow in 1 year discounted at semi annual discount rate

Price of Treasury bond = 10 / (1+0.80%) + 1010 / (1+1%)^2 = 10/1.0080 + 1010 / (1.01)^2 = 9.9206 + 990.0990 = 1000.02

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