资金等值的公式看着比较繁琐,其实能够理解了,就容易掌握了,给大家共享一个事例,希望有所帮助!
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S5ZpÒBÑPç9bbs.3c3t.comFMËk1<S3.2.3 复利计算的基本公式一、一次支付终值公式 终值是指一笔资金在若干计息周期末的期终值,即全部计息周期的本利和。当计算一次偿还本金和累计利息的期终值时,用复利终值公式:
5ZpÒBÑPç9bbs.3c3t.comFMËk1<SF=P(1+i)n (3-1)5ZpÒBÑPç9bbs.3c3t.comFMËk1<S
式中:F--本利和;P--本金;i--利率;n--利息的周期数;(1+i)n-复利系数。系数代号写成(F/P,i,n)。
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S公式可简化成:
5ZpÒBÑPç9bbs.3c3t.comFMËk1<SF=P(F/P,i,n)5ZpÒBÑPç9bbs.3c3t.comFMËk1<S
为了比较简便地使用复利计息的基本公式,一般采用一个规格化代号来代表各个公式中的系数。它的一般形式为(X/y,i%,n),其中X代表要求的数,y代表已知条件。
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S因此,复利系数可表示为:(F/P,i,n),复利终值公式可表示为:F=P(F/P,i,n)。
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S若已知利率、计息周期,直接从查
上查得需要的复利系数值。
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S例1
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S 某建筑公司进行技术改造,今年初向银行贷款100万元,明年初又贷款200万元,年利率6%,复利计息。试问第三年末一次偿还多少万元,并绘出现金流量图。 5ZpÒBÑPç9bbs.3c3t.comFMËk1<S 解:绘出现金流量图,如图3-4所示。5ZpÒBÑPç9bbs.3c3t.comFMËk1<S
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S 图3-45ZpÒBÑPç9bbs.3c3t.comFMËk1<S F=100(1+0.06)3+200(1+0.06)2=119.10+224.72=343.82(万元)5ZpÒBÑPç9bbs.3c3t.comFMËk1<S 或写成:F=P(F/P,i,n) 根据i=6%,n=2,n=3,查,复利系数 =1.1236(n=2),1.191(n=3)5ZpÒBÑPç9bbs.3c3t.comFMËk1<S F=P1(F/P1,6%,3)+ P2(F/P2,6%,2)5ZpÒBÑPç9bbs.3c3t.comFMËk1<S =100×1.191+200×1.12365ZpÒBÑPç9bbs.3c3t.comFMËk1<S =343.82(万元)5ZpÒBÑPç9bbs.3c3t.comFMËk1<S 答:第三年末一次偿还343.82万元。5ZpÒBÑPç9bbs.3c3t.comFMËk1<S
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详细请下载下面附件
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S二、一次支付现值公式 现值是把未来一定时间收支的货币换算成现在时刻的价值。当把一次偿还的期终值折算成现值时,用复利现值公式:
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S 5ZpÒBÑPç9bbs.3c3t.comFMËk1<S (3-2)
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S式中:
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S i--折现率,一般用银行利率为折现率;
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S --现值系数或折现系数。系数代号写成(P/F,i,n)
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S公式可简化成:P=F(P/F,i,n)
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S例2
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S 某建筑构件,预计在今后3年中,每年年末可获得利润100万元,折现率按银行利率6%计,试问相当于现在的多少万元? 5ZpÒBÑPç9bbs.3c3t.comFMËk1<S 解:绘出现金流量图。如图3-5所示。5ZpÒBÑPç9bbs.3c3t.comFMËk1<S
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S 图3-55ZpÒBÑPç9bbs.3c3t.comFMËk1<S 5ZpÒBÑPç9bbs.3c3t.comFMËk1<S 或写成P=F(p/F,i,n) 根据 i=6%,n=1,n=2,n=3,查现值系数分别等于0.9439(n=1),0.8900(n=2),0.8396(n=3)5ZpÒBÑPç9bbs.3c3t.comFMËk1<S P=100(P/F,6%,1)+100(P/F,6%,2)+100(P/F,6%,3)5ZpÒBÑPç9bbs.3c3t.comFMËk1<S =100×0.9439+100×0.8900+100×0.83965ZpÒBÑPç9bbs.3c3t.comFMËk1<S =267.35(万元)5ZpÒBÑPç9bbs.3c3t.comFMËk1<S 答:相当于现值267.3万元。5ZpÒBÑPç9bbs.3c3t.comFMËk1<S
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5ZpÒBÑPç9bbs.3c3t.comFMËk1<S三、年金终值公式(等额支付终值) “年金”是指逐年等额借款或付款的金额。当逐年等额借款.累计一次偿还期终值时,用年金终值公式计算:
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S (3-3)
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S式中:F--指一次偿还期终值或一次提取期终值;
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S A--表示每个计息期末等额借款或等额存款;
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S --年金终值系数。系数代号写成(F/A,i,n)。
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S公式可简化成:
5ZpÒBÑPç9bbs.3c3t.comFMËk1<SF=A(F/A,i,n)5ZpÒBÑPç9bbs.3c3t.comFMËk1<S
例3
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S 某洗衣机厂自筹资金扩建,连续五年每年末从利润中提取100万元存入银行,年利率6%,复利计息。试问五年后能筹集多少万元? 5ZpÒBÑPç9bbs.3c3t.comFMËk1<S 解:绘出现金流量图,如图3-6所示。5ZpÒBÑPç9bbs.3c3t.comFMËk1<S
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S 图3-65ZpÒBÑPç9bbs.3c3t.comFMËk1<S 5ZpÒBÑPç9bbs.3c3t.comFMËk1<S 或写成F=A(F/A,i,n) 根据i=6%,n=5,查年金终值系数=5.63715ZpÒBÑPç9bbs.3c3t.comFMËk1<S F=100(F/A,6%,5)5ZpÒBÑPç9bbs.3c3t.comFMËk1<S =10×5.63715ZpÒBÑPç9bbs.3c3t.comFMËk1<S =563.71(万元)5ZpÒBÑPç9bbs.3c3t.comFMËk1<S 答:五年后筹集资金563.7万元。5ZpÒBÑPç9bbs.3c3t.comFMËk1<S
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5ZpÒBÑPç9bbs.3c3t.comFMËk1<S四、偿债基金公式(等额支付偿债基金)为筹措将来需要的一笔资金,求每个计息期末等额存储的金额数时,用存储基金公式计算:
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S (3-4)
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S式中:F--指一次偿还期终值或一次提取期终值;
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S A--表示每个计息期末等额借款或等额存款;
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S __偿债基金系数;系数代号写成(A/F,i,n)。
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S公式可简化成:
5ZpÒBÑPç9bbs.3c3t.comFMËk1<SA=F(A/F,i,n)5ZpÒBÑPç9bbs.3c3t.comFMËk1<S
例4
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S 某工厂计划五年后设备更新,共需资金300万元,银行利率10%,复利计息。试求该厂每年年末从利润中提取多少万元存储,才能满足需要。 5ZpÒBÑPç9bbs.3c3t.comFMËk1<S 解:绘出现金流量图,如图3-7所示。5ZpÒBÑPç9bbs.3c3t.comFMËk1<S
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S 图3-75ZpÒBÑPç9bbs.3c3t.comFMËk1<S 5ZpÒBÑPç9bbs.3c3t.comFMËk1<S 或写成A=F(A/F,i,n) 根据 i=10%,n=5,查偿债基金系数=0.16385ZpÒBÑPç9bbs.3c3t.comFMËk1<S A=300(A/F,10%,5)5ZpÒBÑPç9bbs.3c3t.comFMËk1<S =300×0.16385ZpÒBÑPç9bbs.3c3t.comFMËk1<S =49.14(万元)5ZpÒBÑPç9bbs.3c3t.comFMËk1<S 答:每年年末存储49.14万元。5ZpÒBÑPç9bbs.3c3t.comFMËk1<S
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5ZpÒBÑPç9bbs.3c3t.comFMËk1<S五、资金还原公式(等额支付资金回收)当借贷一笔资金后,在每年计息周期末等额偿还本利和时,用资金还原公式计算:
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S (3-5)
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S公式推导如下:
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S5ZpÒBÑPç9bbs.3c3t.comFMËk1<S式中:
--资金还原系数,系数代号写成(A/P,i,n)
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S公式可简化成:A=P(A/P,i,n)
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S例5
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S5ZpÒBÑPç9bbs.3c3t.comFMËk1<S六、年金现值公式(等额支付现值)当逐年等额收益(或支付)一笔年金,求此收益(或支付)年金的现值时,用年金现值公式计算:
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S (3-6)
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S公式来源于资金还原公式。
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S式中:
--年金现值系数,系数代号写成:(P/A,i,n)
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S公式可简化成:
5ZpÒBÑPç9bbs.3c3t.comFMËk1<SP=A(P/A,i,n)5ZpÒBÑPç9bbs.3c3t.comFMËk1<S
例6
5ZpÒBÑPç9bbs.3c3t.comFMËk1<S5ZpÒBÑPç9bbs.3c3t.comFMËk1<S