A six-month zero-coupon bond has a price of USD 97, while a 12-month 7.00 Percent annual coupon bond (paid semiannually) has a price of USD 100.50. Both bonds have a face value of USD 100. Find the 12-month spot rate based on annual compounding, semiannual compounding, and continuous compounding:
Step 1: 6 month cashflows are worth 97 Percent of face value --> first coupon = 0.97 x USD 3.5 = USD 3.395 Step 2: 12 month coupon bond is worth USD 100.5 - USD 3.395 = USD 97.105 Step 3: face value including semiannual coupon = USD 100 + USD 3.5 = USD 103.5 Step 4: 12 month cash flows are worth USD 97.205 / USD 103.5 = 0.93821 of face value Step 5: How do I calculate the Spot Rates based on annual compounding, semiannual compounding, and continuous compounding given the discount factor of 0.93821?
Solution: The one-year spot rate can be expressed as 3.98 Percent annually compounded, 3.94 Percent compounded semiannually, or 3.90 Percent compounded continuously. How do I get these values?