#### Roshan Ramdas

##### Active Member

Have 2 queries surrounding the below question from the document qr12.p1.t3.hull_134_185_v5 (page 103).

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Hull.04.03: The 6-month and 1-year zero rates are both 10% per annum. For a bond that has a life of 18 months and pays a coupon of 8% per annum (with semiannual payments and one having just been made), the yield is 10.4% per annum. What is the bond’s price? What is the 18month zero rate? All rates are quoted with semiannual compounding.

Answer: Suppose the bond has a face value of $100. Its price is obtained by discounting the cash flows at 10.4%. The price is 4/1.052 + 4/1.052^2 + 4/1.052^3 = 96.74 If the 18-month zero rate is R, we must have 4/1.05 + 4/1.05^2 + 104/ (1 + R/2)^3 = 96.74 which gives R = 10.42

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1.We seem to have discounted cash flows using the discrete compounding method as opposed to continuous compounding (Cash Flow.e^-yt). Are there any ground rules surrounding the method of discounting to be used please ?

2.Also,...the question specifically highlights that 1 of the semi annual payments have been made I.e., 12 months to maturity.

Yet the bond price being shown in the solution seems to be arrived at by discounting cash flows across all 18 months. Why is this the case please ?

Lastly,...there seems to be a typo with the cash flow received in the last 6 months.....should be 104 as opposed to 4.

Thank you,

Roshan