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Under a Semi-Annual Compounding Convention, the Present Value of A n

Question 8

Multiple Choice

Under a semi-annual compounding convention, the present value of a nn -period cashflow using its ytm yy is given by P=C/(1+y/2) nP = C / ( 1 + y / 2 ) ^ { n } . Which of the following is an equivalent way of expressing the same present value?


A) P=Cdn(n/2) P = C \cdot d _ { n } \cdot ( n / 2 ) , where dnd _ { n } is the discount function for nn periods, and n/2n / 2 is the time to maturity of the cash-flow.
B) P=Cezn×n/2P = C e ^ { - z _ { n } \times n / 2 } , where ZnZ _ { n } is the semi-annual basis zero-coupon rate for nn periods.
C) P=C/j=1n(1+fj) P = C / \prod _ { j = 1 } ^ { n } \left( 1 + f _ { j } \right) , where fjf _ { j } is the forward rate for period jj .
D) None of the above.

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