问题如下图：
选项：
A. 
B. 
C. 
解释：
第一个payment是发生在第十三期期末，为什么第一折现显示的是第十二期
源_品职助教 · 2018年03月14日
因为在后付年金的计算模式下，第一步算得年金的的现值的时间点是在第一笔现金流发生时间点的前一期。在本题中，PV12是在T=12时刻(第一笔现金流发生在T=13时刻)。所以第二步计算T=0时刻的PV0时要往前折现12年，即N=12
yehan99 · 2018年03月28日
这个回答太不负责任了，就不能像何老师一样画个图解释一下
小猕猴 · 2018年03月28日
感觉助教的回答已经很详细很耐心了啊，自己跟着解释画一遍图能理解的更好（第一次用有问必答不小心点成了踩，不好意思啊T T。。。）
源_品职助教 · 2018年03月28日
谢谢你的肯定~熟能生巧，多用几次就上手了。
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
