题目
An investor buys $10,000 face amount of the U.S. Treasury 6 1/2 (coupon rate = 6.50%) of August 15, 2017, for settlement on July 1st, 2014. The last coupon paid on February 15, 2014 and the next coupon pays on August 15, 2014. The bond's yield to maturity happens to be 4.00%. What is nearest to the bond's quoted price at settlement? (this adds a level of difficulty by not giving you the invoice price)
选项
A.$9,338.48
B.$9,904.15
C.$10,095.07
D.$10,726.83
答案
D
解析
We first need the invoice price. We can price the bond as of the last coupon date: PV (at 2/15/2014) = -PV(2.0%, 7, 325, 10000) = $10,809.00,with the calculator: n = 7, I/Y = 2, PMT = 325, FV = 10000 --> CPT PV = $10,809.00Note, from 2/15/14 to 8/15/17 is 3.5 years or 7.0 semesters.Then we can compound this forward to settlement date, with the given yield, such that:Invoice (aka, Full) Price = PV(at 7/1/2014) = $10,809.00 × (1+4%/2) ^ (136/181) = $10,971.03.Finally, we extract the bond's quoted price:As AI = $10,000 × 6.5%/2 × 136/181 = $244.20,Quoted Price = Invoice Price - AI = $10,971.03 - $244.20 = $10,726.83.这道题的计算过程如下：