Under a Semi-Annual Compounding Convention,the Present Value of A $n$ -Period Cashflow Using Its Ytm

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.