这道题为什么N=12呢？我的理解是如果是第13年初的话才是N=12
问题如下图：
选项：
A. 
B. 
C. 
解释：
WINWIN8 · 2018年09月04日
皮一下
帮答
我的理解是， 不管是在13年的年末或者年初，第一笔annuity 2000 都是发生在13年，那13年就不能计入n来算。
菲菲_品职助教 · 2018年09月04日
璐璐，你的理解稍微有一点点小偏差哦，可以看一下我给她的回答哈。如果发生在13年年初的话，就是先付年金了哦。
WINWIN8 · 2018年09月04日
如果发生在13年初就判断为先付年金是因为我们假设了现在就付了买年金的费用吗？
菲菲_品职助教 · 2018年09月04日
不是的，如果题目中有提到说payment发生在年初就是先付。而且年金的费用是从第十三年开始分期付的，不是现在付的哦。
WINWIN8 · 2018年09月04日
菲菲老师，那你看看这道题： An individual wants to be able to spend €80,000 per year for an anticipated 25 years in retirement. To fund this retirement account, he will make annual deposits of €6,608 at the end of each of his working years. He can earn 6% compounded annually on all investments.
WINWIN8 · 2018年09月04日
这道题是问：The minimum number of deposits that are needed to reach his retirement goal is closest to， 那就是分两步算，我的问题是，第一步n=25时，如果判断是用先付还是后付模式来算？
菲菲_品职助教 · 2018年09月04日
其实很明显哦，题目中都会明确表明。比如说这道题说make annual deposits of 6608 at the end of each years，就是后付年金的意思哦。如果是先付的话，题目中会显示at the beginning of 或者说什么pay today之类的。还是很明显的。
WINWIN8 · 2018年09月04日
嗯，那个我知道。 可是这道题是分两步算嘛，第一步是算出n=25，ptm=80000, fv=0, i/y=66,求pv?，我就是不清楚这一步该用先付还是后付模式算？ 然后第二步是题里求出第一步的pv为fv来算，如题目所说at the end of each years就是后付年金的模式算。
菲菲_品职助教 · 2018年09月05日
这个先付和后付是只针对于有PMT的情况哦，也就是你所谓的第一步，也就是每年有payment的这种情况。第二步PMT等于0，不管是先付还是后付算出来的结果都是一样滴～
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
