单击此处编辑母版标题样式,,单击此处编辑母版文本样式,,第二级,,第三级,,第四级,,第五级,,,*,Chapter 5 the valuation of riskless securities,,,Questions and problems,,,group four -------,彭利、蒋英、陈艳,,陈红霖、吴晓琴、邹雨薇、陈园华,,4、Face value = $1000,,n = 3,,a,:①,PV = $816.30,② PV = $949.37 PMT = 70,插补法,,Face value = $1000 PMT = 100 n = 4,b,:①,②,,face value=$1000, i=9%, n=3,,,,PV=$975.13, PMT=1000,×,9%=90,,7.,,face value=$1000, n=3,,,,PV1=$930.23, PV2=$923.79, PV3=$919.54,8.,,9.,,,(1).Three year bonds,:,,,,,,,,The four-year bonds:,,The five-year bonds,,11.,,,12. f,0,1,=S,1,=10.0%, f,1,2,=9.5%,,,f,2,3,=9.0%, f,3,4,=8.5%,(1+S,2,),2,=(1+S,1,)*（1+f,1,2,）,S,2,=9.75%,(1+S,3,),3,=(1+S,2,),2,*(1+f,2,3,),S,3,=9.,5%,(1+S,4,),4,=(1+S,3,),3,*(1+f,3,4,),S,4,=9.25%,,13. S1=f,0,,,1,=6.0%,f,1,2,=9.0%,f,2,3,=10%,,,Face value=$1000,i=8%,n=3,PV=80*0.9434+80*0.8655+1080*0.7868,,=$994.46,,14,.,a,.,,,b:,,c:,,15.,,Effective interest rate=,Semianually,:,,Effective interest rate=,b. Daily :,,Effective interest rate=,,FV=30000 (1+8%),（,1+10%,）,(1+12%)= $ 39916.8,16.a:,PV=$30000,8%,10%,12%,0,1,2,3,b:,PV=$30000,1,3,2,4%,5%,6%,4%,5%,6%,,17.,第一问求：,bank discount rate (BDR),,∵,PV=FV/(1+i),n,, n=2 years,,∴ $9500/,（,1+i),2,= $8000,,,得出,i=9%,第二问求,:the true interest rate,,∵,the true interest rate,,=BDR/(1-BDR),,∴ the true interest rate,,=9%/(1-9%)=9.9%,,,24.,= 5.04%,,27. Assume that you own a bond that you purchased three years ago for $10300. The bond has made three annual interest payments of $700 to you, the last of which was just paid. At the end of year 1 the bond sold for $10100. At the end of year 2, it sold for $9900. The bond now sells for $9500. what was your holding-period return over the three-year period?,V,0,=$10300,INT=$700,$700,$700,P,1,=$10100,P,2,=$9900,P,3,=$9500,,持有期期末价值与期初价值之比：,各时段期末与期初价值之比的积：,方法一：,Value at the end of the holding period,Value at the beginning of the holding period,- 1,,During the first year:,,initial value of bond: V0=$10300,,Value of bond at the end of the year:V1=$700+$10100=$10800,During the second year:,,initial value of bond: V1=$10100,,Value of bond at the end of the year:V2=$700+$9900=$10600,During the third year:,,initial value of bond: V2=$9900,,Value of bond at the end of the year:V3=$700+$9500=$10200,V,0,=$10300,INT=$700,$700,$700,P,1,=$10100,P,2,=$9900,P,3,=$9500,,持有期期末价值与期初价值之比：,Value at the end of the holding period,Value at the beginning of the holding period,- 1,=1.1337-1=13.37%,,方法二：,直接计算出债券在持有期期末的价值。
Step1:,how many bonds you can buy at the end of the first year ?,,You can use the $700 to buy :,$700/$10100= 0.0693,,第二年末收到的利息,=1.0693*700= $748.51,,第二年末持有的债券的价值,=1.0693*9900= $10532.61,So you can obtained,$748.51,in interest in the second year and would have had bonds with a Value of,$10532.61,at the end of the second year.,,Step2:,how many bonds you can buy at the end of the second year ?,,You can use the $748.51 to buy:,$748.51/$9900 =0.0756,,,第三年末收到的利息,= (1.0693+0.0756)*700=$801.43,,第三年末持有的债券的价值：,= (1.0693+0.0756)*9500,,= $10876.55,So you can obtained,$801.43,in interest in the second year and would have had bonds with a Value of,$10876.55,at the end of the third year.,,Step3:,,计算持有期期末价值,,value at the end of the holding period,,=$801.43+$10876.55=$11677.98,$11677.98/$10300,–,1,,= 0.1337,,= 13.37%,Value at the end of the holding period,Value at the beginning of the holding period,- 1,,Holding-period return can be converted to an equivalent return for each period (,r,g,) .,,。