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

question 5

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.

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