My Math Forum Quoted price of a bond?

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 December 2nd, 2009, 11:18 PM #1 Newbie   Joined: Dec 2009 Posts: 1 Thanks: 0 Quoted price of a bond? What is a quoted price of a bond? Is it a clean price? I think it is the present value of the face value of a bond, am I correct? What is the quoted price of a bond that has 4.5 years until maturity? The face value of the bond is \$5,000 and it has a coupon rate of 8.1% compounded semi-annually and a yield rate of 8.6% compounded semi-annually. Here's what I did: Using the formula of PV=FV(1 + i)^-n 5000(1 + 0.043)^-9 5000(0.068460682) 3,423.03 But given the multiple choice answers I have, I am wrong. The choices were: 4908.32, 4888.32, 4898.32, 4998.32 or 4809.32 I would appreciate any help/insight. Thanks
 December 4th, 2009, 06:19 PM #2 Newbie   Joined: Dec 2008 From: Copenhagen, Denmark Posts: 29 Thanks: 0 Re: Quoted price of a bond? In Europe, the quoted price of a bond is usually the bonds "dirty price", meaning that the quote consists of the present value of all future payments + accrued interest. This is not really important in this question, since accrued interest is zero (a coupon has just been paid, since coupons are semi-annually and maturity is 4,5 years). The bonds price quote is, since accrued interest is zero, the present value of all future payments. Now it's not really clear how the exact payment profile is, based on the questions description of the bond, but the most usual (especially in the US) is a bullet bond, meaning that only coupons will be payed on the given payment dates, except for the maturity date for which both a coupon and the bond face value will be paid. Let's assume this is the payment profile for our bond. We have 9 payment dates. and the first 8 of these are coupons $c= \frac{0,081 \cdot 5000}{2} = 202,5$ and the last payment is a coupon plus the face value, let's call this $F= 5202,5$. Let's call the semi-annual discount rate $r= \frac{0,086}{2} = 0,043$ Now we can find the present value as $\begin{equation*} price = PV = \sum_{i=1}^8 c \cdot (1+r)^{-i} \quad + \quad F \cdot (1+r)^{-9} \quad = \quad \sum_{i=1}^8 202,5 \cdot 1,043^{-i} \quad + \quad 5202,5 \cdot 1,043^{-9} \quad = \quad {4908.32} \end{equation}$

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# quoted price of bond

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