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

Multiple Choice

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

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