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1、Chapter 3,Time Value of Money,Pearson Education Limited 2004Fundamentals of Financial Management,12/eCreated by:Gregory A.Kuhlemeyer,Ph.D.Carroll College,Waukesha,WI,播匿算筹坏毛狄菩逾抒酗钟嗜碴庭裴又疑凛馈刷琼逗豪烫腻酒牡滁埠山撤精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,After studying Chapter 3,you should be able to:,Un
2、derstand what is meant by the time value of money.Understand the relationship between present and future value.Describe how the interest rate can be used to adjust the value of cash flows both forward and backward to a single point in time.Calculate both the future and present value of:(a)an amount
3、invested today;(b)a stream of equal cash flows(an annuity);and(c)a stream of mixed cash flows.Distinguish between an“ordinary annuity”and an“annuity due.”Use interest factor tables and understand how they provide a shortcut to calculating present and future values.Use interest factor tables to find
4、an unknown interest rate or growth rate when the number of time periods and future and present values are known.Build an“amortization schedule”for an installment-style loan.,薯缸森捕惠办寒颗跺不彭嘉厕酵钱颗绽盗测俗阑龄裤柱沁歹鬼恬缅宁县僧精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,The Time Value of Money,The Interest Rate
5、Simple Interest Compound Interest Amortizing a LoanCompounding More Than Once per Year,黑吟挨教毕腋矩陈饲喻巴冬苫铱封享山灵靴赵竭益仗悯砂寂啼奠络诲贰涣精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,Obviously,$10,000 today.You already recognize that there is TIME VALUE TO MONEY!,The Interest Rate,Which would you prefer-$10,000
6、 today or$10,000 in 5 years?,苔颧悼能吕锹壬钒销刷科戴份缉纬究垦绑胰尉舌阅甸罚片斩脊志粥酉吧液精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,TIME allows you the opportunity to postpone consumption and earn INTEREST.,Why TIME?,Why is TIME such an important element in your decision?,追砖谰悸概锯缅锨录泡含矮陪圆鸥嫉休矿溪雀胸兵雍讯游便苑榜跪赔楷漾精品课程财务管理基础英文课件
7、ch03Van Horne/Wachowicz Tenth Edition,Types of Interest,Compound InterestInterest paid(earned)on any previous interest earned,as well as on the principal borrowed(lent).,Simple InterestInterest paid(earned)on only the original amount,or principal,borrowed(lent).,朝羽锦嚷撕羞敞负逾互纲贾扔慎坯意围益君育裔避懒委珊锈殃屯牙胳衡需精品课程财
8、务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,Simple Interest Formula,FormulaSI=P0(i)(n)SI:Simple InterestP0:Deposit today(t=0)i:Interest Rate per Periodn:Number of Time Periods,垃裕雇贼薪芬轻逗衔汉窗引寄预惟桶雍讣铃毡绝佑堑赢氟瓣劣矢壶甜乞典精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,SI=P0(i)(n)=$1,000(.07)(2)=$140,Simpl
9、e Interest Example,Assume that you deposit$1,000 in an account earning 7%simple interest for 2 years.What is the accumulated interest at the end of the 2nd year?,疲山埋靴弄员豪开瞄翼铲土赛毙癌刃媳种秦士贷估晌著刨倦熬受唤讼芽碧精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,FV=P0+SI=$1,000+$140=$1,140Future Value is the value a
10、t some future time of a present amount of money,or a series of payments,evaluated at a given interest rate.,Simple Interest(FV),What is the Future Value(FV)of the deposit?,闷开卷孽从酞唐汰蔼秩晚梦目换影秒臻讯打棋程送仍贼钦缅举袜怎钎鸥左精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,The Present Value is simply the$1,000 you or
11、iginally deposited.That is the value today!Present Value is the current value of a future amount of money,or a series of payments,evaluated at a given interest rate.,Simple Interest(PV),What is the Present Value(PV)of the previous problem?,宾儿莆杯欧焦储尹琅肆疏晾卑即谎凤妈零奎僵琶番禾启摆僧妻杭骂阅额眩精品课程财务管理基础英文课件ch03Van Horne/
12、Wachowicz Tenth Edition,Why Compound Interest?,Future Value(U.S.Dollars),毖下前鞘辟薪凭匙壬丰鹰豁漠怪阐糟陌叉蚀捡背锄漾童涂捂砂叠裹阉铡京精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,Assume that you deposit$1,000 at a compound interest rate of 7%for 2 years.,Future ValueSingle Deposit(Graphic),0 1 2,$1,000,FV2,7%,双掀沽云纯梳绽滓困宴繁
13、裁哀拟抉闸选哄独云烂染奶馋凹彬粉酉比景汛惫精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,FV1=P0(1+i)1=$1,000(1.07)=$1,070Compound InterestYou earned$70 interest on your$1,000 deposit over the first year.This is the same amount of interest you would earn under simple interest.,Future ValueSingle Deposit(Formula),寇淫哺
14、卡渡筋歧艺百帅效汛撮随昼拼铰泽谦宴喳嚏花战祈捣狞晾限鸦戚辞精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,FV1=P0(1+i)1=$1,000(1.07)=$1,070FV2=FV1(1+i)1=P0(1+i)(1+i)=$1,000(1.07)(1.07)=P0(1+i)2=$1,000(1.07)2=$1,144.90You earned an EXTRA$4.90 in Year 2 with compound over simple interest.,Future ValueSingle Deposit(Formula),耀贸
15、妖嘱矽恶京预涯樊瓤肆载躇徽饭呀颖擎秘曳米胸走碗鲁曼性喇环寓沙精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,FV1=P0(1+i)1FV2=P0(1+i)2General Future Value Formula:FVn=P0(1+i)n or FVn=P0(FVIFi,n)-See Table I,General Future Value Formula,etc.,昔唉告陋迂幻熏啪饶赶待象美紊练孙燃续趋摸铰惑耸探赛梢协抽抄启注兽精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,FVI
16、Fi,n is found on Table I at the end of the book.,Valuation Using Table I,运卧假歪拥佃索乏伤刑劝蓖袱阉举翱梯值睡注郭勺捉潮障河覆辨阑焦位技精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,FV2=$1,000(FVIF7%,2)=$1,000(1.145)=$1,145 Due to Rounding,Using Future Value Tables,割播拯客码高潘敏洲捏教囱嵌衅墟蝴壤景氦国措橙帜更纤极问昼逃落俘输精品课程财务管理基础英文课件ch03Van Horne
17、/Wachowicz Tenth Edition,TVM on the Calculator,Use the highlighted row of keys for solving any of the FV,PV,FVA,PVA,FVAD,and PVAD problems,N:Number of periodsI/Y:Interest rate per periodPV:Present valuePMT:Payment per periodFV:Future valueCLR TVM:Clears all of the inputs into the above TVM keys,殴辈晨撒
18、琳卧锯频帮让喇凡口骆切犀的逾剑油哑舜是俊椎塘考慌柴刑殷谨精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,Using The TI BAII+Calculator,N,I/Y,PV,PMT,FV,Inputs,Compute,Focus on 3rd Row of keys(will be displayed in slides as shown above),陷俐序誉窄牛慢狞故温惺惋诚韧溉鳃茶溃酌帆姐糠喂炸斤谷袋戳幼钥骨我精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,Enterin
19、g the FV Problem,Press:2nd CLR TVM2 N7 I/Y-1000 PV0 PMT CPT FV,抛帚葡嘴狠蔼毙差朴蹬繁雪扫登买银阵滩嫉娘雅段症寂末吴慌铰万蚕咀磕精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,N:2 Periods(enter as 2)I/Y:7%interest rate per period(enter as 7 NOT.07)PV:$1,000(enter as negative as you have“less”)PMT:Not relevant in this situation(
20、enter as 0)FV:Compute(Resulting answer is positive),Solving the FV Problem,N,I/Y,PV,PMT,FV,Inputs,Compute,2 7-1,000 0,1,144.90,唯栋萧牧敖澎傲弟捂阅幢收怕辽叮潞半挑耶芹侨它延酒蜕誊省毁磊缮哩服精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,Julie Miller wants to know how large her deposit of$10,000 today will become at a compoun
21、d annual interest rate of 10%for 5 years.,Story Problem Example,0 1 2 3 4 5,$10,000,FV5,10%,押洗煞宪祷厢绵獭哎隋碱恰墨赂陌废贯抵彤涡扫呐肛存盂疗克恕穗擞斡袋精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,Calculation based on Table I:FV5=$10,000(FVIF10%,5)=$10,000(1.611)=$16,110 Due to Rounding,Story Problem Solution,Calculatio
22、n based on general formula:FVn=P0(1+i)n FV5=$10,000(1+0.10)5=$16,105.10,唇蚂女候怀扯即哮揍爵完搓碍愈恋瞳忠祸到歌局闯舅颂族钮范估粪衅咕困精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,Entering the FV Problem,Press:2nd CLR TVM5 N 10 I/Y-10000 PV0 PMT CPT FV,曼弘蒸镶呢虐述涝律粥肃斟基烫渺膜单团肤弄诛咆帅驶汗诸剧筷币凝防搞精品课程财务管理基础英文课件ch03Van Horne/Wachowicz T
23、enth Edition,The result indicates that a$10,000 investment that earns 10%annually for 5 years will result in a future value of$16,105.10.,Solving the FV Problem,N,I/Y,PV,PMT,FV,Inputs,Compute,5 10-10,000 0,16,105.10,承佰罚菊玉恬盗钡簧付裔似戍具吭攒深牟堡扯耘招币赦没嚏迭移眼址殊堵精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,
24、We will use the“Rule-of-72”.,Double Your Money!,Quick!How long does it take to double$5,000 at a compound rate of 12%per year(approx.)?,乍缚疡陡近继伪井歼东驯棉知旧拆频缸汽季衍此腊逝赊侯铡摩蔫侵剧苗废精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,Approx.Years to Double=72/i%72/12%=6 YearsActual Time is 6.12 Years,The“Rule-of-
25、72”,Quick!How long does it take to double$5,000 at a compound rate of 12%per year(approx.)?,扩贡扰妖性芭卫自裸陡栽贪察垮知德忽椭堤彬柞伏铂锥顷魂趋球咯挫转便精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,The result indicates that a$1,000 investment that earns 12%annually will double to$2,000 in 6.12 years.Note:72/12%=approx.6
26、years,Solving the Period Problem,N,I/Y,PV,PMT,FV,Inputs,Compute,12-1,000 0+2,000,6.12 years,擂瘩侨笼始蝴藉殆携恫辛瘟襟鼎椒音韵破碍砂骄醇售倪装嘴逐驭娱配鼓缮精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,Assume that you need$1,000 in 2 years.Lets examine the process to determine how much you need to deposit today at a discount
27、 rate of 7%compounded annually.,0 1 2,$1,000,7%,PV1,PV0,Present Value Single Deposit(Graphic),滥瘪躲锗凝严刮蒜拘潮梗炸切姆萨喳梳液沁墓咕禁捌衅诧炬惶菲聋恨封仓精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,PV0=FV2/(1+i)2=$1,000/(1.07)2=FV2/(1+i)2=$873.44,Present Value Single Deposit(Formula),0 1 2,$1,000,7%,PV0,搀言热瘁绊征它膊爽堕票蚀锰衍筐
28、灿归迎坪限锑臀暮掏莹支沤磅港伯峭化精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,PV0=FV1/(1+i)1PV0=FV2/(1+i)2General Present Value Formula:PV0=FVn/(1+i)n or PV0=FVn(PVIFi,n)-See Table II,General Present Value Formula,etc.,推琐躇惹叫濒敛说土涂印谤牺怔杠卜控同琼岿抡停含垄诊婪望烘挎旦斑搞精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,PVIFi,
29、n is found on Table II at the end of the book.,Valuation Using Table II,领酿抡渗朱揖积溯碰懊诡娜件婉始造劲鞘融泼竿击代氯毙篇娠蜜花潘验哼精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,PV2=$1,000(PVIF7%,2)=$1,000(.873)=$873 Due to Rounding,Using Present Value Tables,应止婪镑巨惰咆悸啪携皖兑批队搏派岗饱壮办幂锡输炽伪匝肢咋邮退澄逊精品课程财务管理基础英文课件ch03Van Horne/Wa
30、chowicz Tenth Edition,N:2 Periods(enter as 2)I/Y:7%interest rate per period(enter as 7 NOT.07)PV:Compute(Resulting answer is negative“deposit”)PMT:Not relevant in this situation(enter as 0)FV:$1,000(enter as positive as you“receive$”),Solving the PV Problem,N,I/Y,PV,PMT,FV,Inputs,Compute,2 7 0+1,000
31、,-873.44,存气藕纠肌狮脖翼沂硝发漏她翟抡獭行银栋断胸跟榴奏趋禽铁勃和褐淀益精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,Julie Miller wants to know how large of a deposit to make so that the money will grow to$10,000 in 5 years at a discount rate of 10%.,Story Problem Example,0 1 2 3 4 5,$10,000,PV0,10%,歼恢槛赦换迟闲暑浊终枝火灵殊载峻屯书迫肋乎救姨
32、艰猩氢呀戏旧丛胡镶精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,Calculation based on general formula:PV0=FVn/(1+i)n PV0=$10,000/(1+0.10)5=$6,209.21Calculation based on Table I:PV0=$10,000(PVIF10%,5)=$10,000(.621)=$6,210.00 Due to Rounding,Story Problem Solution,冤揖音怪敖户梭坐迈游斑凳糖慨捡靠催瞄驱曾发嗽般畔镰趁步斯杖仁锚喊精品课程财务管理基
33、础英文课件ch03Van Horne/Wachowicz Tenth Edition,Solving the PV Problem,N,I/Y,PV,PMT,FV,Inputs,Compute,5 10 0+10,000,-6,209.21,The result indicates that a$10,000 future value that will earn 10%annually for 5 years requires a$6,209.21 deposit today(present value).,喳郑康课柞箕字俐阴吮悉轨锥斜咎哩窝丧脱炊唾经搬毫佰曝括框贪碑康匆精品课程财务管理基础
34、英文课件ch03Van Horne/Wachowicz Tenth Edition,Types of Annuities,Ordinary Annuity:Payments or receipts occur at the end of each period.Annuity Due:Payments or receipts occur at the beginning of each period.,An Annuity represents a series of equal payments(or receipts)occurring over a specified number of
35、 equidistant periods.,牡雇置好贤敛诗辖治剁择枢甸阶曼岩灭申领寇敬轩沙纲惧扶甭容浦匠贬禹精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,Examples of Annuities,Student Loan Payments Car Loan Payments Insurance Premiums Mortgage Payments Retirement Savings,肾隧芒野从库插冰棋告哮铆过跪卤揉件煎钠戳尧醒著穷牌山炉般琳切稀锁精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth
36、Edition,Parts of an Annuity,0 1 2 3,$100$100$100,(Ordinary Annuity)End ofPeriod 1,End ofPeriod 2,Today,Equal Cash Flows Each 1 Period Apart,End ofPeriod 3,珍咖澜怜闰娱迭督科涧沤赴字践汹岂津歉乓婪治粟悍翘炕磁塑累牡愁滋健精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,Parts of an Annuity,0 1 2 3,$100$100$100,(Annuity Due)Beginni
37、ng ofPeriod 1,Beginning ofPeriod 2,Today,Equal Cash Flows Each 1 Period Apart,Beginning ofPeriod 3,唬凉况误专偿少渔梆庞谋垛蔓涂磷刮掂几峡参欧控怕昨铰携侦默溢先渡寥精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,FVAn=R(1+i)n-1+R(1+i)n-2+.+R(1+i)1+R(1+i)0,Overview of an Ordinary Annuity-FVA,R R R,0 1 2 n n+1,FVAn,R=Periodic Cash
38、 Flow,Cash flows occur at the end of the period,i%,.,掩扎惠这桅昂献东诛专唯爬恫郡泡缉宵枉沥柔阔眶戏交青吕谅砷持汐忽董精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,FVA3=$1,000(1.07)2+$1,000(1.07)1+$1,000(1.07)0=$1,145+$1,070+$1,000=$3,215,Example of anOrdinary Annuity-FVA,$1,000$1,000$1,000,0 1 2 3 4,$3,215=FVA3,7%,$1,070,$1,
39、145,Cash flows occur at the end of the period,亡马逊束妇宿梯坯耀硫俘适近洋寡料指遏窝亮耙惮她采彬寒录甄海民侩蒜精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,Hint on Annuity Valuation,The future value of an ordinary annuity can be viewed as occurring at the end of the last cash flow period,whereas the future value of an annuit
40、y due can be viewed as occurring at the beginning of the last cash flow period.,硬趟棉读湿疫矣瘟匀涯夯边计涉柏沾讶瓜慧漳迢侣梁凿寒正站临丹旦叭绩精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,FVAn=R(FVIFAi%,n)FVA3=$1,000(FVIFA7%,3)=$1,000(3.215)=$3,215,Valuation Using Table III,遁焉己布猛事嗅工镊麦甥貉踪礁灭窘瞧冯镣俐草猛狮咸些仟帐敛烤吝灶休精品课程财务管理基础英文课件ch0
41、3Van Horne/Wachowicz Tenth Edition,N:3 Periods(enter as 3 year-end deposits)I/Y:7%interest rate per period(enter as 7 NOT.07)PV:Not relevant in this situation(no beg value)PMT:$1,000(negative as you deposit annually)FV:Compute(Resulting answer is positive),Solving the FVA Problem,N,I/Y,PV,PMT,FV,Inp
42、uts,Compute,3 7 0-1,000,3,214.90,绰稳蒙龋奈玄码阴音僚垢井帧垃辩哺疡炯济茁谜翘缮特掠肖咳框败峦拔拌精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,FVADn=R(1+i)n+R(1+i)n-1+.+R(1+i)2+R(1+i)1=FVAn(1+i),Overview View of anAnnuity Due-FVAD,R R R R R,0 1 2 3 n-1 n,FVADn,i%,.,Cash flows occur at the beginning of the period,涝钝林俏驭葬术囊活饰眨胰
43、孪秽匝健骑报邯遏湛悼你釜跌反醒信随而瑚桥精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,FVAD3=$1,000(1.07)3+$1,000(1.07)2+$1,000(1.07)1=$1,225+$1,145+$1,070=$3,440,Example of anAnnuity Due-FVAD,$1,000$1,000$1,000$1,070,0 1 2 3 4,$3,440=FVAD3,7%,$1,225,$1,145,Cash flows occur at the beginning of the period,条错胰翰书袍佑隅怀
44、劈疆伐斑恳斩龋顽融瞧恒她钮殖卯亚扫举仓抬喜板股精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,FVADn=R(FVIFAi%,n)(1+i)FVAD3=$1,000(FVIFA7%,3)(1.07)=$1,000(3.215)(1.07)=$3,440,Valuation Using Table III,堆迎曰遏诊涣钱愁陡擞窃森甩友颧塌同邮悸刚硅涤间肿做伴便掩溢硫哭惑精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,Solving the FVAD Problem,N,I/Y,PV,P
45、MT,FV,Inputs,Compute,3 7 0-1,000,3,439.94,Complete the problem the same as an“ordinary annuity”problem,except you must change the calculator setting to“BGN”first.Dont forget to change back!Step 1:Press2ndBGNkeysStep 2:Press2ndSETkeysStep 3:Press2ndQUITkeys,独韧管撵爆活阔腰晨能宾裕换侵月纷鹿葵聪铰恋枉愧疯酝夕缔迅乐符产余精品课程财务管理基础英
46、文课件ch03Van Horne/Wachowicz Tenth Edition,PVAn=R/(1+i)1+R/(1+i)2+.+R/(1+i)n,Overview of anOrdinary Annuity-PVA,R R R,0 1 2 n n+1,PVAn,R=Periodic Cash Flow,i%,.,Cash flows occur at the end of the period,珍警万邑装凤丁裙稠墒谦另拉旁幻幌姬肘胜哎炔阐隆橙柱臃妓筹河唾冀架精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,PVA3=$1,000/(1.
47、07)1+$1,000/(1.07)2+$1,000/(1.07)3=$934.58+$873.44+$816.30=$2,624.32,Example of anOrdinary Annuity-PVA,$1,000$1,000$1,000,0 1 2 3 4,$2,624.32=PVA3,7%,$934.58$873.44$816.30,Cash flows occur at the end of the period,逾末摈钎腺信蔽救铂橇氓夫篆连既途邮宠谬郡斤零摄详肪懦铁碉妮呆猛湍精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,Hi
48、nt on Annuity Valuation,The present value of an ordinary annuity can be viewed as occurring at the beginning of the first cash flow period,whereas the future value of an annuity due can be viewed as occurring at the end of the first cash flow period.,已馁镭鸳陶拜韧购据正右区桓柜倚企厂勋凡控客冒中工里棚喷美宰集涧傅精品课程财务管理基础英文课件ch0
49、3Van Horne/Wachowicz Tenth Edition,PVAn=R(PVIFAi%,n)PVA3=$1,000(PVIFA7%,3)=$1,000(2.624)=$2,624,Valuation Using Table IV,艾乓涩嘲毫乔采蛛按拢咒搅切汾佣箍汗额帚篮蚊瞥订晃妊诞劝辜洗宅仗互精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,N:3 Periods(enter as 3 year-end deposits)I/Y:7%interest rate per period(enter as 7 NOT.07)PV:Co
50、mpute(Resulting answer is positive)PMT:$1,000(negative as you deposit annually)FV:Not relevant in this situation(no ending value),Solving the PVA Problem,N,I/Y,PV,PMT,FV,Inputs,Compute,3 7-1,000 0,2,624.32,澈惦寒丫媳嘿诞废广懊倡酞膀辩渭郊骋呆治柑暑绞暂递八拥瞒铸疲掀穿判精品课程财务管理基础英文课件ch03Van Horne/Wachowicz Tenth Edition,PVADn=R/(1
