版權(quán)說(shuō)明:本文檔由用戶提供并上傳,收益歸屬內(nèi)容提供方,若內(nèi)容存在侵權(quán),請(qǐng)進(jìn)行舉報(bào)或認(rèn)領(lǐng)
文檔簡(jiǎn)介
1、CHAPTER4InterestRatesPracticeQuestionsProblem4.1.Abankquotesyouaninterestrateof7%perannumwithquarterlycompounding.Whatistheequivalentratewith(a)continuouscompoundingand(b)annualcompounding?(a) Theratewithcontinuouscompoundingis(0074In1+二0.0694I4丿or6.94%perannum.(b) Theratewithannualcompoundingisor7.
2、19%perannum.Problem4.2.ExplainhowLIBORisdetermined(0.07¥1+亍丿-1=0.0719LIBORistheLondonInterBankOfferedRate.ItiscalculateddailyfromborrowingratesestimatedbyapanelofbanksProblem4.3.Thesix-monthandone-yearzeroratesareboth5%perannum.Forabondthathasalifeof18monthsandpaysacouponof4%perannum(withsemian
3、nualpaymentsandonehavingjustbeenmade),theyieldis5.2%perannum.Whatisthebond'sprice?Whatisthe18-monthzerorate?Allratesarequotedwithsemiannualcompounding.Supposethebondhasafacevalueof$100.Itspriceisobtainedbydiscountingthecashflowsat5.2%.Thepriceis22102+1.0261.02621.0263=98.29Ifthe18-monthzeroratei
4、sR,wemusthave22+1.0251.0252102(1+R/2)3二98.29whichgivesR=5.204%.Problem4.4.Aninvestorreceives$1,100inoneyearinreturnforaninvestmentof$1,000now.Calculatethepercentagereturnperannumwitha)annualcompounding,b)semiannualcompounding,c)monthlycompoundingandd)continuouscompounding.(a) Withannualcompoundingth
5、ereturnis1100-1二0.11000or10%perannum.(b) Withsemi-annualcompoundingthereturnisRwhere(R)210001+_=1100I2丿i.e.,R1+£11二1.04882sothatR=0.0976.Thepercentagereturnistherefore9.76%perannum.(c) WithmonthlycompoundingthereturnisRwhere(R)1210001+=1100I12丿i.e.1+A=血皿797sothatR=0.0957.Thepercentagereturnisth
6、erefore9.57%perannum.(d) WithcontinuouscompoundingthereturnisRwhere:1000eR=1100i.e.,eR=1.1sothatR=ln1.1=0.0953.Thepercentagereturnistherefore9.53%perannum.Problem4.5.Supposethatzerointerestrateswithcontinuouscompoundingareasfollows:Maturity(months)Rate(%perannum)33.063.293.4123.5153.6183.7Calculatef
7、orwardinterestratesforthesecond,third,fourth,fifth,andsixthquarters.TheforwardrateswithcontinuouscompoundingareasfollowstoQtr23.4%Qtr33.8%Qtr43.8%Qtr54.0%Qtr64.2%Problem4.6.Assumingthatrisk-freeratesareasinProblem4.5,whatisthevalueofanFRAwheretheholderwillpayLIBORandreceive4.5%(quarterlycompounded)f
8、orathree-monthperiodstartinginoneyearonaprincipalof$1,000,000.TheforwardLIBORrateforthethreemonthperiodis5%quarterlycompounded.Fromequation(4.9),thevalueoftheFRAistherefore1,000,000X0.25X(0.045-0.050)e-0.036x1.25二-1,195or$1,195Problem4.7.Thetermstructureofinterestratesisupwardsloping.Putthefollowing
9、inorderofmagnitude:(a) Thefive-yearzerorate(b) Theyieldonafive-yearcoupon-bearingbond(c) Theforwardratecorrespondingtotheperiodbetween4.75and5yearsinthefutureWhatistheanswertothisquestionwhenthetermstructureofinterestratesisdownwardsloping?Whenthetermstructureisupwardsloping,c>a>b.Whenitisdown
10、wardsloping,b>a>c.Problem4.8.Whatdoesdurationtellyouaboutthesensitivityofabondportfoliotointerestrates?Whatarethelimitationsofthedurationmeasure?Durationprovidesinformationabouttheeffectofasmallparallelshiftintheyieldcurveonthevalueofabondportfolio.Thepercentagedecreaseinthevalueoftheportfolio
11、equalsthedurationoftheportfoliomultipliedbytheamountbywhichinterestratesareincreasedinthesmallparallelshift.Thedurationmeasurehasthefollowinglimitation.Itappliesonlytoparallelshiftsintheyieldcurvethataresmall.Problem4.9.Whatrateofinterestwithcontinuouscompoundingisequivalentto8%perannumwithmonthlyco
12、mpounding?TherateofinterestisRwhere:i.e.,(0.08)12eR=1+I12丿R二12lnfi+008I12丿=0.0797Therateofinterestistherefore7.97%perannum.Problem4.10.Adepositaccountpays4%perannumwithcontinuouscompounding,butinterestisactuallypaidquarterly.Howmuchinterestwillbepaideachquarterona$10,000deposit?Theequivalentrateofin
13、terestwithquarterlycompoundingisRwhereeo.04=orR二4(eo.o1-1)二0.0402Theamountofinterestpaideachquarteristherefore:0.040210,ooox-:二100.504or$100.50.Problem4.11.Supposethat6-month,12-month,18-month,24-month,and30-monthzeroratesare,respectively,4%,4.2%,4.4%,4.6%,and4.8%perannumwithcontinuouscompounding.Es
14、timatethecashpriceofabondwithafacevalueof100thatwillmaturein30monthsandpayacouponof4%perannumsemiannually.Thebondpays$2in6,12,18,and24months,and$102in30months.Thecashpriceis2e-0.04x0.5+2e-0.042x1.0+2e-0.044x1.5+2e-0.046x2+102e-0.048x2.5=98.04Problem4.12.Athree-yearbondprovidesacouponof8%semiannually
15、andhasacashpriceof104.Whatisthebond'syield?Thebondpays$4in6,12,18,24,and30months,and$104in36months.Thebondyieldisthevalueofythatsolves4e-0.5y+4e-1.0y+4e-1.5y+4e-2.0y+4e-2.5y+104e-3.0y=104UsingtheSolverorGoalSeektoolinExcel,y=0.06407or6.407%.Problem4.13.Supposethatthe6-month,12-month,18-month,and
16、24-monthzeroratesare5%,6%,6.5%,and7%respectively.Whatisthetwo-yearparyield?Usingthenotationinthetext,m=2,d=e-0.07x2=0.8694.AlsoA=e-0.05x0.5+e-0.06x1.0+e-0.065x1.5+e-0.07x2.0=3.6935Theformulainthetextgivestheparyieldas(100-100x0.8694)x2=7創(chuàng)3.6935_*Toverifythatthisiscorrectwecalculatethevalueofabondtha
17、tpaysacouponof7.0741%peryear(thatis3.5370everysixmonths).Thevalueis3.537e-0.05x0.5+3.537e-0.06x1.0+3.537e-0.065x1.5+103.537e-0.07x2.0=100verifyingthat7.0741%istheparyield.Problem4.14.Supposethatrisk-freezerointerestrateswithcontinuouscompoundingareasfollows:Maturity(years)Rate(%perannum)12.023.033.7
18、44.254.5Calculateforwardinterestratesforthesecond,third,fourth,andfifthyears.Theforwardrateswithcontinuouscompoundingareasfollows:Year2:4.0%Year3:5.1%Year4:5.7%Year5:5.7%Problem4.15.Usetherisk-freeratesinProblem4.14tovalueanFRAwhereyouwillpay5%(compoundedannually)andreceiveLIBORforthethirdyearon$1mi
19、llion.TheforwardLIBORrate(annuallycompounded)forthethirdyearis5.5%.WevaluetheFRAbyassumingthattheforwardLIBORwillberealized.ThevalueoftheFRAis1,000,000x(0.0550.050).637x3=$4,474.69Problem4.16.A10-year,8%couponbondcurrentlysellsfor$90.A10-year,4%couponbondcurrentlysellsfor$80.Whatisthe10-yearzerorate
20、?(Hint:Considertakingalongpositionintwoofthe4%couponbondsandashortpositioninoneofthe8%couponbonds.)Takingalongpositionintwoofthe4%couponbondsandashortpositioninoneofthe8%couponbondsleadstothefollowingcashflowsYear0:90一2x80=-70Year10:200-100=100becausethecouponscancelout.$100in10yearstimeisequivalent
21、to$70today.The10-yearrate,R,(continuouslycompounded)isthereforegivenby100=70e10RTherateis丄in100二0.03571070or3.57%perannumProblem4.17.Explaincarefullywhyliquiditypreferencetheoryisconsistentwiththeobservationthatthetermstructureofinterestratestendstobeupwardslopingmoreoftenthanitisdownwardsloping.Ifl
22、ong-termratesweresimplyareflectionofexpectedfutureshort-termrates,wewouldexpectthetermstructuretobedownwardslopingasoftenasitisupwardsloping.(Thisisbasedontheassumptionthathalfofthetimeinvestorsexpectratestoincreaseandhalfofthetimeinvestorsexpectratestodecrease).Liquiditypreferencetheoryarguesthatlo
23、ngtermratesarehighrelativetoexpectedfutureshort-termrates.Thismeansthatthetermstructureshouldbeupwardslopingmoreoftenthanitisdownwardsloping.Problem4.18.“Whenthezerocurveisupwardsloping,thezerorateforaparticularmaturityisgreaterthantheparyieldforthatmaturity.Whenthezerocurveisdownwardsloping,thereve
24、rseistrue.”Explainwhythisisso.Theparyieldistheyieldonacoupon-bearingbond.Thezerorateistheyieldonazero-couponbond.Whentheyieldcurveisupwardsloping,theyieldonanN-yearcoupon-bearingbondislessthantheyieldonanN-yearzero-couponbond.ThisisbecausethecouponsarediscountedatalowerratethantheN-yearrateanddragth
25、eyielddownbelowthisrate.Similarly,whentheyieldcurveisdownwardsloping,theyieldonanN-yearcouponbearingbondishigherthantheyieldonanN-yearzero-couponbond.Problem4.19.WhyareU.S.Treasuryratessignificantlylowerthanotherratesthatareclosetoriskfree?Tworeasonsgiveninthechapterare1.Theamountofcapitalabankisreq
26、uiredtoholdtosupportaninvestmentinTreasurybillsandbondsissubstantiallysmallerthanthecapitalrequiredtosupportasimilarinvestmentinothervery-low-riskinstruments.2.IntheUnitedStates,Treasuryinstrumentsaregivenafavorabletaxtreatmentcomparedwithmostotherfixed-incomeinvestmentsbecausetheyarenottaxedatthest
27、atelevel.Problem4.20.Whydoesaloanintherepomarketinvolveverylittlecreditrisk?Arepoisacontractwhereaninvestmentdealerwhoownssecuritiesagreestosellthemtoanothercompanynowandbuythembacklaterataslightlyhigherprice.Theothercompanyisprovidingaloantotheinvestmentdealer.Thisloaninvolvesverylittlecreditrisk.I
28、ftheborrowerdoesnothonortheagreement,thelendingcompanysimplykeepsthesecurities.Ifthelendingcompanydoesnotkeeptoitssideoftheagreement,theoriginalownerofthesecuritieskeepsthecash.Problem4.21.ExplainwhyanFRAisequivalenttotheexchangeofafloatingrateofinterestforafixedrateofinterest?AFRAisanagreementthata
29、certainspecifiedinterestrate,R,willapplytoacertainKprincipal,L,foracertainspecifiedfuturetimeperiod.SupposethattherateobservedinthemarketforthefuturetimeperiodatthebeginningofthetimeperiodprovestobeR.IftheMFRAisanagreementthatRwillapplywhentheprincipalisinvested,theholderoftheKFRAcanborrowtheprincip
30、alatRandtheninvestitatR.ThenetcashflowattheendofMKtheperiodisthenaninflowofRLandanoutflowofRL.IftheFRAisanagreementthatKMRwillapplywhentheprincipalisborrowed,theholderoftheFRAcaninvesttheKborrowedprincipalatR.ThenetcashflowattheendoftheperiodisthenaninflowofMRLandanoutflowofRL.Ineithercaseweseethatt
31、heFRAinvolvestheexchangeofaMKfixedrateofinterestontheprincipalofLforafloatingrateofinterestontheprincipal.Problem4.22.Afive-yearbondwithayieldof7%(continuouslycompounded)paysan8%couponattheendofeachyear.a) Whatisthebond'sprice?b) Whatisthebond'sduration?c) Usethedurationtocalculatetheeffecto
32、nthebond'spriceofa0.2%decreaseinitsyield.d)Recalculatethebond'spriceonthebasisofa6.8%perannumyieldandverifythattheresultisinagreementwithyouranswerto(c).a) Thebond'spriceis8e-0.07+8e-0.07x2+8e-omx3+8e-0.07x4+108e-0.07x5二103.05b) Thebond'sdurationis18e-0.07+2x8e-0.07x2+3x8e-0.07x3+4x8
33、e-0.07x4+5x108e-0.07x5103.05J=4.3235yearsc) Since,withthenotationinthechapterAB二-BDAytheeffectonthebond'spriceofa0.2%decreaseinitsyieldis103.05x4.3235x0.002=0.89Thebond'spriceshouldincreasefrom103.05to103.94d) Witha6.8%yieldthebond'spriceis8e-0.068+8e-0.068x2+8e-0.068x3+8e-0.068x4+108e-0
34、.068x5二103.95Thisisclosetotheanswerin(c).Problem4.23.Thecashpricesofsix-monthandone-yearTreasurybillsare94.0and89.0.A1.5-yearTreasurybondthatwillpaycouponsof$4everysixmonthscurrentlysellsfor$94.84.Atwo-yearTreasurybondthatwillpaycouponsof$5everysixmonthscurrentlysellsfor$97.12.Calculatethesix-month,
35、one-year,1.5-year,andtwo-yearTreasuryzerorates.The6-monthTreasurybillprovidesareturnof6/94=6.383%insixmonths.Thisis2x6.383=12.766%perannumwithsemiannualcompoundingor2ln(1.06383)=12.38%perannumwithcontinuouscompounding.The12-monthrateis11/89=12.360%withannualcompoundingorln(1.1236)=11.65%withcontinuo
36、uscompounding.Forthe1+yearbondwemusthave24e-0.1238x0.5+4e-0.1165x1+104e-1.5r=94.84whereRisthe1十yearzerorate.Itfollowsthat23.76+3.56+104e-1.5r=94.84e-1.5R=0.8415R=0.115or11.5%.Forthe2-yearbondwemusthave5e-0.1238x0.5+5e-0.1165x1+5e-0.115x1.5+105e-2r=97.12whereRisthe2-yearzerorate.Itfollowsthate-2R=0.7
37、977R=0.113or11.3%.Problem4.24.“Aninterestrateswapwheresix-monthLIBORisexchangedforafixedrate5%onaprincipalof$100millionforfiveyearsisaportfolioofnineFRAs.”Explainthisstatement.Thefirstexchangeofpaymentsisknown.EachsubsequentexchangeofpaymentsisanFRAwhereinterestat5%isexchangedforinterestatLIBORonapr
38、incipalof$100million.InterestrateswapsarediscussedfurtherinChapter7.FurtherQuestionsProblem4.25.Whencompoundedannuallyaninterestrateis11%.Whatistheratewhenexpressedwith(a)semiannualcompounding,(b)quarterlycompounding,(c)monthlycompounding,(d)weeklycompounding,and(e)dailycompounding.Wemustsolve1.11=(
39、1+R/n)nwhereRistherequiredrateandthenumberoftimesperyeartherateiscompounded.Theanswersarea)10.71%,b)10.57%,c)10.48%,d)10.45%,e)10.44%Problem4.26.ThefollowingtablegivesTreasuryzeroratesandcashflowsonaTreasurybond:Maturity(yearsZerorateCouponpaymentPrincipal0.52.0%$201.02.3%$201.527%$202.03.2%$20$1000
40、Zeroratesarecontinuouslycompounded(a) Whatisthebond'stheoreticalprice?(b)Whatisthebond'syieldassumingthebondsellsforitstheoreticalprice?Thebond'stheoreticalpriceis2Oxe-o.o2xo.5+2Oxe-o.o23xi+2Oxe-o.o27xi.5+lO2Oxe-o.o32x2=1015.32Thebond'syieldassumingthatitsellsforitstheoreticalpriceis
41、obtainedbysolving20xe-yx0.5+20xe-yxi+20xe-yxi.5+1020xe-yx2=1015.32Itis3.18%.Problem4.27.(Excelfile)Afive-yearbondprovidesacouponof5%perannumpayablesemiannually.Itspriceis104.Whatisthebond'syield?YoumayfindExcel'sSolveruseful.Theanswer(withcontinuouscompounding)is4.07%Problem4.28(Excelfile)Su
42、pposethat3-month,6-month,12-month,2-year,and3-yearOISratesare2.0%,2.5%,3.2%,4.5%,and5%,respectively.The3-month,6-monthand12-monthOISsinvolveasingleexchangeatmaturity;the2-yearand3-yearOISsinvolvequarterlyexchanges.Thecompoundingfrequenciesusedforexpressingtheratescorrespondtothefrequencyofexchanges.
43、CalculatetheOISzeroratesusingcontinuouscompounding.Interpolatelinearlybetweencontinuouslycompoundedratestodetermineratesbetween6monthsand12months,between12monthsand2years,andbetween2yearsand3years.YoumayfindExcel'sSolveruseful.Thetwo-yearandthreeyearOISratesareparyields.Thecalculationsareindicat
44、edontheExcelfile.The3-month,6-month,12-month,2-yearand3-yearzeroratesare1.9950%,2.4845%,3.1499%,4.5153%,and5.0264%,respectively.ThecalculationscanalsobecarriedoutwithDerivaGem.Problem4.29.Aninterestrateisquotedas5%perannumwithsemiannualcompounding.Whatistheequivalentratewith(a)annualcompounding,(b)m
45、onthlycompounding,and(c)continuouscompounding?2.5%ispaideverysixmonths.a) Withannualcompoundingtherateis1.0252-1=0.050625or5.0625%b) Withmonthlycompoundingtherateis12x(1.0251/6-1)=0.04949or4.949%.c) Withcontinuouscompoundingtherateis2xln1.025=0.04939or4.939%.Problem4.30.The6-month,12-month.18-month,
46、and24-monthzeroratesare4%,4.5%,4.75%,and5%withsemiannualcompounding.a) Whataretherateswithcontinuouscompounding?b) Whatistheforwardrateforthesix-monthperiodbeginningin18months?c) Whatisthetwo-yearparyield?a) Withcontinuouscompoundingthe6-monthrateis2ln1.02=0.039605or3.961%.The12-monthrateis2ln1.0225
47、=0.044501or4.4501%.The18-monthrateis2ln1.02375=0.046945or4.6945%.The24-monthrateis2ln1.025=0.049385or4.9385%.b) Theforwardrate(expressedwithcontinuouscompounding)isfromequation(4.5)4.9385x2-4.6945x1.505or5.6707%.Whenexpressedwithsemiannualcompoundingthisis2(e0.056707x0.5-1)=0.057518or5.7518%.c) Thef
48、ormulafortheparyieldis(100-100d)mc=AInthiscased=(1/1.025)4=0.90595,m=2andA=丄+-+-+-=3.77481.021.022521.0237531.0254sothatc=(10°一9°.595)x2=4.9833.7748or4.983%.Bydefinitionthisisalsotheyieldonatwo-yearbondthatpaysacouponequaltotheparyield.Problem4.31.Supposethatrisk-freeratesareasinProblem4.3
49、0.WhatisthevalueofanFRAwheretheholderpaysLIBORandreceives7%(semiannuallycompounded)forasix-monthperiodbeginningin18months.Thecurrentforwardrateforthisperiodis6%(semiannuallycompounded).Theprincipalis$10millionThevalueoftheFRAis10,000,000x(0.070.06)x0.5x1=45,2981.0254or$45,298.Problem4.32.Thefollowin
50、gtablegivesthepricesofbondsBondPrincipal($)TimetoMaturity(yrs)AnnualCoupon($)*BondPrice($)1000.50.0981001.00.0951001.56.21011002.0&0104*Halfthestatedcouponispaideverysixmonthsa) Calculatezeroratesformaturitiesof6months,12months,18months,and24months.b) Whataretheforwardratesfortheperiods:6monthst
51、o12months,12monthsto18months,18monthsto24months?c) Whatarethe6-month,12-month,18-month,and24-monthparyieldsforbondsthatprovidesemiannualcouponpayments?d) Estimatethepriceandyieldofatwo-yearbondprovidingasemiannualcouponof7%perannum.a) Thezerorateforamaturityofsixmonths,expressedwithcontinuouscompoun
52、dingis21n(l+2/98)=4.0405%.Thezerorateforamaturityofoneyear,expressedwithcontinuouscompoundingisln(1+5/95)=5.1293.The1.5-yearrateisRwhere3.1e-0.040405x0.5+3.1e-0.051293x1+103.1e-Rx1.5-101ThesolutiontothisequationisR=0.054429.The2.0-yearrateisRwhere4e-0.040405x0.5+4e-0.051293x1+4e-0.054429x1.5+104e-Rx
53、2=104ThesolutiontothisequationisR=0.058085.TheseresultsareshowninthetablebelowMaturity(yrs)ZeroRate(%)ForwardRate(%)ParYield(s.a.%)Paryield(c.c%)0.54.04054.04054.08164.04051.05.12936.21815.18135.11541.55.44296.07005.49865.42442.05.80856.90545.86205.7778b) Thecontinuouslycompoundedforwardratescalcula
54、tedusingequation(4.5)areshowninthethirdcolumnofthetablec) Theparyield,expressedwithsemiannualcompounding,canbecalculatedfromtheformulainSection4.6.Itisshowninthefourthcolumnofthetable.Inthefifthcolumnofthetableitisconvertedtocontinuouscompoundingd) Thepriceofthebondis3.5e-0.040405x0.5+3.5e-0.051293x
55、1+3.5e-0.054429x1.5+103.5e-0.058085x2=102.13Theyieldonthebond,ysatisfies3.5e-yx0.5+3.5e-yx1.0+3.5e-yx1.5+103.5e-yx2.0=102.13Thesolutiontothisequationisy=0.057723.Thebondyieldistherefore5.7723%.Problem4.33.PortfolioAconsistsofaone-yearzero-couponbondwithafacevalueof$2,000anda10-yearzero-couponbondwit
56、hafacevalueof$6,000.PortfolioBconsistsofa5.95-yearzero-couponbondwithafacevalueof$5,000.Thecurrentyieldonallbondsis10%perannum.(a) Showthatbothportfolioshavethesameduration.(b) Showthatthepercentagechangesinthevaluesofthetwoportfoliosfora0.1%perannumincreaseinyieldsarethesame.(c) Whatarethepercentag
57、echangesinthevaluesofthetwoportfoliosfora5%perannumincreaseinyields?a)ThedurationofPortfolioAis1x2000e-0.1x1+10x6000e-o.ixio=5.952OOOe-o.ixi+6OOOe-o.ixioSincethisisalsothedurationofPortfolioB,thetwoportfoliosdohavethesameduration.b)ThevalueofPortfolioAis2OOOe-o.i+6OOOe-o.ixio=4Oi6.95WhenyieldsincreasebyiObasispointsitsvaluebecomes2OOOe-o.ioi+6OOOe-o.ioixio二3993.i8Thepercentagedecreaseinvalueis23.77xiOO4Oi6.95二O.59%ThevalueofPortfolioBis5OOOe-o.ix5.95二2757.8iWhenyieldsincrease
溫馨提示
- 1. 本站所有資源如無(wú)特殊說(shuō)明,都需要本地電腦安裝OFFICE2007和PDF閱讀器。圖紙軟件為CAD,CAXA,PROE,UG,SolidWorks等.壓縮文件請(qǐng)下載最新的WinRAR軟件解壓。
- 2. 本站的文檔不包含任何第三方提供的附件圖紙等,如果需要附件,請(qǐng)聯(lián)系上傳者。文件的所有權(quán)益歸上傳用戶所有。
- 3. 本站RAR壓縮包中若帶圖紙,網(wǎng)頁(yè)內(nèi)容里面會(huì)有圖紙預(yù)覽,若沒(méi)有圖紙預(yù)覽就沒(méi)有圖紙。
- 4. 未經(jīng)權(quán)益所有人同意不得將文件中的內(nèi)容挪作商業(yè)或盈利用途。
- 5. 人人文庫(kù)網(wǎng)僅提供信息存儲(chǔ)空間,僅對(duì)用戶上傳內(nèi)容的表現(xiàn)方式做保護(hù)處理,對(duì)用戶上傳分享的文檔內(nèi)容本身不做任何修改或編輯,并不能對(duì)任何下載內(nèi)容負(fù)責(zé)。
- 6. 下載文件中如有侵權(quán)或不適當(dāng)內(nèi)容,請(qǐng)與我們聯(lián)系,我們立即糾正。
- 7. 本站不保證下載資源的準(zhǔn)確性、安全性和完整性, 同時(shí)也不承擔(dān)用戶因使用這些下載資源對(duì)自己和他人造成任何形式的傷害或損失。
最新文檔
- 科技公司商業(yè)模式創(chuàng)新的成功案例研究
- 科技助力構(gòu)建平安校園新生態(tài)
- 家庭教育與醫(yī)療健康的關(guān)系
- DB6103T 81-2025袋栽銀耳栽培技術(shù)規(guī)范
- DB35T 2228-2024科技成果轉(zhuǎn)化效果評(píng)估導(dǎo)則
- 個(gè)人向企業(yè)租賃設(shè)備合同標(biāo)準(zhǔn)范本
- 個(gè)人地下停車(chē)位轉(zhuǎn)讓合同書(shū)
- 三人共同持股合同范例
- 個(gè)人貸款合同樣本(房產(chǎn)抵押)
- 二人合資創(chuàng)業(yè)合同書(shū):經(jīng)營(yíng)合作協(xié)議
- 國(guó)家中小學(xué)智慧教育平臺(tái)推動(dòng)家校共育
- 《馬克思主義與社會(huì)科學(xué)方法論》授課教案
- 一個(gè)28歲的漂亮小媳婦在某公司打工-被老板看上之后
- 《線性代數(shù)》課后習(xí)題答案
- 馬工程教育哲學(xué)課件第十章 教育哲學(xué)與教師發(fā)展
- 三年級(jí)道德與法治下冊(cè)第一單元我和我的同伴教材解讀新人教版
- GB/T 11376-2020金屬及其他無(wú)機(jī)覆蓋層金屬的磷化膜
- 成功源于自律 主題班會(huì)課件(共34張ppt)
- 新青島版(五年制)五年級(jí)下冊(cè)小學(xué)數(shù)學(xué)全冊(cè)導(dǎo)學(xué)案(學(xué)前預(yù)習(xí)單)
- (完整word版)重點(diǎn)監(jiān)管的危險(xiǎn)化學(xué)品名錄(完整版)
- 高級(jí)工程師電子版職稱(chēng)證書(shū)在網(wǎng)上打印步驟
評(píng)論
0/150
提交評(píng)論