工程经济学(第三章).ppt

工程经济学 罗云峰 系统工程研究所 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 第三章 资金的时间价值 与等值计算 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 第一节 资金的时间价值与等值计算的概念 一、资金的时间价值概念 将资金投入使用后经过一段时间，资金便 产生了增值，也就是说，由于资金在生产 和流通环节中的作用，使投资者得到了收 益或盈利。不同时间发生的等额资金在价 值上的差别，就是资金的时间价值。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 一、资金的时间价值概念 在工程技术经济分析中，对资金时间价值 的计算方法与银行利息的计算方法是相同 的，银行利息就是一种资金时间价值的表 现形式。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 一、资金的时间价值概念 在商品经济条件下，资金在生产与交换过 程的运动中产生了增值，给投资者带来利 润，其实质是由于劳动者在生产过程中创 造了价值。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 一、资金的时间价值概念 从投资者的角度看，资金的增值特性使资 金具有时间价值。 从消费者的角度来看，资金的时间价值是 对放弃现时消费带来的损失所做的必要补 偿，这是因为资金用于投资后则不能再用 于现时消费。个人储蓄和国家积累的目的 也是如此。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 一、资金的时间价值概念 资金时间价值的大小主要取决于投资收益 率、通货膨胀率和项目投资的风险。 资金的时间价值是工程技术经济分析中重 要的基本原理之一，是用动态分析法对项 目投资方案进行对比、选择的依据和出发 点。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 二、资金等值计算的概念 资金的时间价值表明，在不同的时间付出 或得到同样数额的资金，其经济价值是不 等的。 资金等值是指在时间因素的作用下，在不 同时期(时点)绝对值不等的资金具有相等 的经济价值。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 二、资金等值计算的概念 在比较工业项目或技术方案时，需要对项 目或方案的各项投资与收益进行对比，而 这些投资或收益往往发生在不同的时期， 于是就必须将其按照一定的利率折算至某 一相同时点，进行等值计算，使之具有可 比性。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 第二节 利息、利率及其计算 如果将一笔资金存人银行(相当于银行占用 了这笔资金)，经过了一段时间以后资金 所有者就能在该笔资金之外再得到一些报 酬，我们称之为利息。 式中Fn为本利和，P为本金，In为利息。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 利息通常由本金和利率计算得出，利率是 指在一个计息周期内所应付出的利息额与 本金之比，一般以百分数表示： 式中：i为利率，I1为一个计息周期的利息。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 一、单利与复利 1.单利法 单利法是每期均按原始本金计息，即不管计 息周期为多少，每经一期按原始本金计息一 次，利息不再生利息。单利计息的计算公式 为 In为n个计息期的总利息，n为计息期数，i为 利率。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 1.单利法 N个计息周期后的本利和为 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 单利法的本金、利息和本利和 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 2.复利法 复利法按本利和计息，也就是说除了本金 计息外，利息也生利息，每一计息周期的 利息都要并入下一期的本金，再计利息。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 2.复利法 例如：现有一笔本金P在年利率是i的条件下 ，当计息期数为n时，则本利和Fn为 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 复利法的本金、利息和本利和 年份本金当年利息本利和 1100010000.06601060 2100010600.0663.61123.6 310001123.60.0667.421191.02 410001191.020.0671.461262.48 510001262.480.0675.751338.23 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 复利法与单利法的比较(i i=20%) 年份本金当年利息本利和 1100010000.202001200 2100012000.202401440 3100014400.202881728 4100017280.20345.62073.6 510002073.60.20414.722488. 32 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 复利法与单利法的比较(i i=6%，n n=20) 年份本金当年利息本利和 1100010000.06601060 1010001689.40.06101.361790.85 2010003025.600.06181.543207.14 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 复利法与单利法的比较(i i=20% ，n n=20) 年份本金当年利息本利和 1100010000.202001200 1010005159.780.201031.956191.74 20100031948.000.206389.60 38337.60 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 由于实际占用资金的情况正是复利所表达 的，复利计算更符合资金在社会再生产过 程中运动的实际，因此，工程经济分析中 一般采用复利计算。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 二、名义利率与实际利率 当利率的时间单位与计息周期不一致时， 同样的年利率下，不同计息周期所得的利 息不同，这是因为名义利率与实际利率不 同。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 二、名义利率与实际利率 名义利率是计息周期的利率与一年的计息 次数之乘积。 若按单利计息，名义利率与实际利率是一 致的。但按复利计算，名义利率与实际利 率则不相等。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 若名义利率为r，一年中计息次数为n，那么 ，一个计息周期的利率就为r/n，一年后的 本利和为： 利息为 实际利率i为 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 名义利率与实际利率的换算公式为： Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 不同计息周期的年实际利率价 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 三、间断计息与连续计息 复利计息有间断复利和连续复利之分。如果 计息周期为一定的时间(如年、季、月)，并 按复利计息，称为间断计息。如果计息周期 缩短，短到任意长的时期均可，也就是无限 缩短，则称为连续复利。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 对于名义利率r，若在一年中使计息次数无 限多，也就是使计息周期无限小，就可得 出连续复利的一次性支付计算公式为 当 时，按连续复利计算，实际利率 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 例 31 某企业投资项目需要向银行贷款200万元， 年利率为10，试用间断计息法和连续计 息法分别计算5年后的本利和。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 第二节 资金的等值计算 资金等值是指在考虑了时间因素之后，在 不同时刻发生的数值不等的资金可能具有 相等的价值。由于资金时间价值的存在， 不同时刻发生的资金支出或收入不能直接 相加，为了达到资金的流入或流出满足时 间可比性要求，就必须进行资金的等值计 算。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 资金的等值是考虑了资金时间价值后的等 值。资金数额相等，发生的时间不同，其 价值并不一定相等；而资金数额不等，但 发生的时间也不同，其价值却可能相等。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 决定资金等值的因素有三： 资金数额； 资金发生的时刻； 利率。 其中利率是关键性因素，在考察资金 等值的问题中通常都以相同利率作为依据 进行比较计算。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 例如，某用户以年利率8借款1000元，借 期5年，有四种偿付方法： Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 利用等值概念，把不同时点发生的资金金 额换算成同一时点的等值金额，这一过程 叫做资金等值计算。 把将来某一时点的资金金额换算成现在的 等值金额的换算过程称为“折现”或“贴 现”。与现值等价的将来某个时点的资金 价值称为“终值”或“未来值”。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 一、整付类型 整付是指在分析经济系统现金流量时，现 金流入或流出均在一个时点发生。在考虑 资金时间价值的情况下，现金流入F只与现 金流出P相等，则P与F就是等值的。P是F 的现值，F是P的终值。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 1. 整付终值公式 整付终值是指期初投资P元，利率为i，在第 n年末一次偿还本利和F。 整付终值公式为： 在等值计算中，系数(1+i)n是一种复合利率( 简称复利)，称为整付终值系数，记为(F/P, i, n)，其数值可以从复利表查到。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 已知参数 待求参数 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 例 32 某公司决定进入新领域进行项目开发，需 向银行贷款100万元，年利率为12%，借期4 年，4年后向银行偿付本利和为多少？ Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 2.整付现值公式 已知终值F，求现值P的等值公式，整付现 值公式是它是整付终值的逆运算： 系数 称为整付现值系数，记为 (P/F,i,n) Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. (P/F,i,n)和(F/P,i,n)互为倒数，即 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 例 33 某用户为孩子8年后可以得到30000元的教 育基金，现应存入多少资金？年利率为6% 。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 二、等额分付类型 大多数现金流量是分布在整个分析期内的 ，即多次支付。现金流入和流出发生在多 个时点的现金流量，其数额可以是不等的 ，也可以是相等的。当现金流序列是连续 的，且数额相等，则称为等额序列现金流 。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 1.等额分付终值计算公式 对于一个经济系统，在每一个计息周期期 末支付相同的数额A，年利率为i的情况下， 求与n年内系统的总现金流出等值的系统现 金流入，即求取系统n年后一次支付的终值 ，就是等额分付终值计算问题。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 等额分付终值计算公式的现金流量简图 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 等额分付终值计算公式的现金流量简图 等额分付终值计算公式等额分付终值计算公式 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 称为等额分付终值系数，记为 (F/A,i,n); 应用 应满足： (1)每期支付金额相同(A值)； (2)支付间隔相同(如一年)； (3)每次支付都在对应的期末，终值与最后 一期支付同时发生。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 例34 某高速公路的贷款投资部分为15亿元，5年 建成，每年年末贷款投资3亿元，若年利率 是8%，求5年后实际累计总投资额。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 例 35 按政府有关规定，贫困学生在大学学习期 间可享受政府贷款。某大学生在大学四年 学习期间，每年年初从银行贷款7000元用 以支付当年学费及部分生活费用，若年利 率为5，则此学生4年后毕业时借款本息 一共是多少？ Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 2.等额分付偿债基金公式 在年利率为i的情况下，欲将第n年年末的资 金F换算为与之等值的n年中每年年末的等 额资金，这就是等额分付偿债基金计算问 题。显见，等额分付偿债基金的计算是等 额分付终值计算的逆运算，于是可得到公 式 称为等额分付偿债基金系数， 记为(A/F,i,n)。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 例 36 某企业计划自筹资金进行一项技术改造， 预计5年后进行的这项改造需要资金300万 元，银行利率8，问今年起每年末应筹集 多少？ Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 3.等额分付现值计算公式 对于工程项目，在第1年年初投资为P，从 第1年年末取得效益，考虑资金的时间价值 ，在年利率为i的情况下，已知n年中每年末 所获效益均为A，从第1年到第n年的等额现 金流入总额等值于最初的现金流出P，欲求 投资P，这就是等额分付现值计算问题。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 等额分付类型的现金流量图 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 等额分付现值公式： 其中， 称为等额分付现值系数， 记为(P/A,i,n) Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 例 37 一俱乐部会员每年的会费是9000元，一期5 年，如果该俱乐部实施先付费后活动，加 入俱乐部时须一次预存一期的费用，那么 在年利率7的情况下，现应预存多少钱？ Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 例 38 如果某工程当年建成，第二年投产开始有 收益，寿命期为8年，每年净收益为3万元 ，按12的折现率计算，恰好能在寿命期 内把期初投资全部收回。试问，该工程期 初所投资金为多少？ Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 例 39 某科技工业园设立每年50万元的奖学金， 以投资教育。在年利率为10的条件下， 试求这笔奖学金永久年金的现值。 Evaluation only.Evaluation only. Creat