问题如下图：
选项：
A. 
B. 
C. 
为什么我们在计算Pv 时候，假设FV为0？ 解释：
星星_品职助教 · 2019年12月11日
同学你好，
以年金为例，年金有的其实只是一系列等额等间距的现金流，也就是PMT，在年金的0时点，和最后一期N时点，是没有除了PMT以外的现金流的。也就是说，PV和FV都是根据这些PMT求出来的，而不是本来就存在的现金流。如以下第一张图。
所以当求PV的时候，由于N时点没有（除PMT以外）的现金流，这个时候FV就是0，如以下第二张图。
当求FV时，由于0时点也没有现金流，所以这个时候PV=0。如以下第三张图。
但有一种情况FV是不为0的，就是固收里即将学到的债券，因为在N时点是有一笔面值（par value）要付的，所以除了PMT外还有一笔现金流，这个时候按计算器的时候，FV不是0，而是Par value 的值。如以下第四张图。
加油~
NO.PZ2015120604000013问题如下 annuity of $2,000 per yewill receivefor twenty years. The first payment is to receivethe enof thirteenth years. Assume the scount rate is 7% over next years, calculate the toy's present value of the annuityA.$8,792.B.$9,408.C.$10,066. B is correct. Calculate the PV of annuity the enof the twentieth years : N = 20; I/Y = 7; PMT = -2,000; FV = 0; CPT PV = 21,188.03. ; Calculate the PV toy: N = 12; PMT = 0; FV = -21,188.03; I/Y = 7; CPT PV = 9,407.74. 这题时间线没看懂能不能一下
NO.PZ2015120604000013问题如下annuity of $2,000 per yewill receivefor twenty years. The first payment is to receivethe enof thirteenth years. Assume the scount rate is 7% over next years, calculate the toy's present value of the annuityA.$8,792.B.$9,408.C.$10,066. B is correct. Calculate the PV of annuity the enof the twentieth years : N = 20; I/Y = 7; PMT = -2,000; FV = 0; CPT PV = 21,188.03. ; Calculate the PV toy: N = 12; PMT = 0; FV = -21,188.03; I/Y = 7; CPT PV = 9,407.74. 如題 看不懂toy的時刻
NO.PZ2015120604000013 问题如下 annuity of $2,000 per yewill receivefor twenty years. The first payment is to receivethe enof thirteenth years. Assume the scount rate is 7% over next years, calculate the toy's present value of the annuity A.$8,792. B.$9,408. C.$10,066. B is correct. Calculate the PV of annuity the enof the twentieth years : N = 20; I/Y = 7; PMT = -2,000; FV = 0; CPT PV = 21,188.03. ; Calculate the PV toy: N = 12; PMT = 0; FV = -21,188.03; I/Y = 7; CPT PV = 9,407.74. 是否可以这样理解第一步求出的13时点的PV实际是12时点的年末值FV，第二步往前折的起算点得从12时点算，所以才是N=12
NO.PZ2015120604000013 问题如下 annuity of $2,000 per yewill receivefor twenty years. The first payment is to receivethe enof thirteenth years. Assume the scount rate is 7% over next years, calculate the toy's present value of the annuity A.$8,792. B.$9,408. C.$10,066. B is correct. Calculate the PV of annuity the enof the twentieth years : N = 20; I/Y = 7; PMT = -2,000; FV = 0; CPT PV = 21,188.03. ; Calculate the PV toy: N = 12; PMT = 0; FV = -21,188.03; I/Y = 7; CPT PV = 9,407.74. 之前也有一个说first payment in 5 quarters. 这道题是 first payment will happen the enof 13th year,都是求PV。 所以怎么理解这个first payment与present的关系，这个first payment都是未来发生的情况？这道题里面，如果first payment是在第十三年发生， 那么之前是没有现金流入的呀。the beginning of the 13th year应该是时点零，算这个时点的PV的话，N等于8， I/Y=7，PMT=-20000，FV=0。然后这个PV等于十二年后的FV，再折现得到现在的PV？如果按照答案解析里面，开始算PV就是N=20，那等于说在开始12年都是有payment的，跟题干要求不一致呢，怎么理解呢？
NO.PZ2015120604000013 问题如下 annuity of $2,000 per yewill receivefor twenty years. The first payment is to receivethe enof thirteenth years. Assume the scount rate is 7% over next years, calculate the toy's present value of the annuity A.$8,792. B.$9,408. C.$10,066. B is correct. Calculate the PV of annuity the enof the twentieth years : N = 20; I/Y = 7; PMT = -2,000; FV = 0; CPT PV = 21,188.03. ; Calculate the PV toy: N = 12; PMT = 0; FV = -21,188.03; I/Y = 7; CPT PV = 9,407.74. 老师，我实在绕不过来，很笨地画了一个图，如图，在第13年底收到第一笔2000，往后收20次。第一步折现到PV13，我没有问题，第二步折现到0时刻，这个箭头怎么数都是13个啊，所以我觉得N应该是13