为什么这题学费不是用bgn模式？而有的题目需要
问题如下图：
选项：
A. 
B. 
C. 
解释：
菲菲_品职助教 · 2018年11月20日
同学你好，题目的意思相当于在T=18的时候开始交50,000这一笔钱，要交四年，所以要先对这四笔钱折现。具体如下图所示：
由图可知，这里的第一笔50,000发生在18年末19年初，“in 18 years”可以看出来，即在T=18时交第一笔钱，折现之后算出的PV其实是T=17时的PV。N=4; I/Y=6; FV=0; PMT=50,000; CPT PV=173255.28
因为题目要求的是今天应该存多少钱，然后再进行下一步折现，STEP 2: N=17; PMT=0; I/Y=6; FV=173255.28; CPT PV=64340.85，即本题的答案。
学费确实是一个先付的概念，但在这道题里面，先付是体现在，她是在18年初即17年末一次性付清学费，因为我们把学费都折现到17年末了。但是单单就计算而言，还是要用后付年金的方式来计算。但其实这道题你用先付年金来计算也是可以的，相当于第一步，算出来的PV是T=18时刻的，即183650.5975。然后再进行第二步计算，但是这里就要注意N=18而不是17了。
其实两种方法都能算出答案，关键就在于从哪个角度来理解题目。然后画出时间轴，注意细节就可以了！
姿姿不倦 · 2018年12月01日
讲得很好，谢谢菲菲！
菲菲_品职助教 · 2018年12月01日
考试加油！～
ss_liu · 2018年12月05日
请问既然交学费是在期初 那为什么不是在18年初交呢 看图解实际是在18年末交
菲菲_品职助教 · 2018年12月06日
我在解释里面已经写的很详细了噢，解释了先付体现在哪里。
NO.PZ2017092702000014 问题如下 Granarents are funng a newborn’s future university tuition costs, estimate$50,000/yefor four years, with the first payment e a lump sum in 18 years. Assuming a 6% effective annurate, the requireposit toy is closest to: A.$60,699. B.$64,341. C.$68,201. B is correct. First, finthe present value (PV) of ornary annuity in Ye17 threpresents the tuition costs: 50,000[1−1(1+0.06)40.06]50,000{\lbrack\frac{1-\frac1{{(1+0.06)}^4}}{0.06}\rbrack}50,000[0.061−(1+0.06)41] = $50,000 × 3.4651 = $173,255.28. Then, finthe PV of the annuity in toy’s llars (where FV is future value):PV0=FV(1+0.06)17=173,255.28(1+0.06)17PV_0=\frac{FV}{{(1+0.06)}^{17}}=\frac{173,255.28}{{(1+0.06)}^{17}}PV0=(1+0.06)17FV=(1+0.06)17173,255.28PV0 = $64,340.85 ≈ $64,341. 173255.28我能算出来 但为什么下一步时间是17 不是18
NO.PZ2017092702000014 问题如下 Granarents are funng a newborn’s future university tuition costs, estimate$50,000/yefor four years, with the first payment e a lump sum in 18 years. Assuming a 6% effective annurate, the requireposit toy is closest to: A.$60,699. B.$64,341. C.$68,201. B is correct. First, finthe present value (PV) of ornary annuity in Ye17 threpresents the tuition costs: 50,000[1−1(1+0.06)40.06]50,000{\lbrack\frac{1-\frac1{{(1+0.06)}^4}}{0.06}\rbrack}50,000[0.061−(1+0.06)41] = $50,000 × 3.4651 = $173,255.28. Then, finthe PV of the annuity in toy’s llars (where FV is future value):PV0=FV(1+0.06)17=173,255.28(1+0.06)17PV_0=\frac{FV}{{(1+0.06)}^{17}}=\frac{173,255.28}{{(1+0.06)}^{17}}PV0=(1+0.06)17FV=(1+0.06)17173,255.28PV0 = $64,340.85 ≈ $64,341. N=18， I/Y= 6， PMT=0, FV = 200000 这样哪里错了
NO.PZ2017092702000014问题如下Granarents are funng a newborn’s future university tuition costs, estimate$50,000/yefor four years, with the first payment e a lump sum in 18 years. Assuming a 6% effective annurate, the requireposit toy is closest to:A.$60,699.B.$64,341.C.$68,201.B is correct. First, finthe present value (PV) of ornary annuity in Ye17 threpresents the tuition costs: 50,000[1−1(1+0.06)40.06]50,000{\lbrack\frac{1-\frac1{{(1+0.06)}^4}}{0.06}\rbrack}50,000[0.061−(1+0.06)41] = $50,000 × 3.4651 = $173,255.28. Then, finthe PV of the annuity in toy’s llars (where FV is future value):PV0=FV(1+0.06)17=173,255.28(1+0.06)17PV_0=\frac{FV}{{(1+0.06)}^{17}}=\frac{173,255.28}{{(1+0.06)}^{17}}PV0=(1+0.06)17FV=(1+0.06)17173,255.28PV0 = $64,340.85 ≈ $64,341.first payment e，这里的e不是先付吗？如果不是，那么 题干一般如何表达先付呢？
NO.PZ2017092702000014 问题如下 Granarents are funng a newborn’s future university tuition costs, estimate$50,000/yefor four years, with the first payment e a lump sum in 18 years. Assuming a 6% effective annurate, the requireposit toy is closest to: A.$60,699. B.$64,341. C.$68,201. B is correct. First, finthe present value (PV) of ornary annuity in Ye17 threpresents the tuition costs: 50,000[1−1(1+0.06)40.06]50,000{\lbrack\frac{1-\frac1{{(1+0.06)}^4}}{0.06}\rbrack}50,000[0.061−(1+0.06)41] = $50,000 × 3.4651 = $173,255.28. Then, finthe PV of the annuity in toy’s llars (where FV is future value):PV0=FV(1+0.06)17=173,255.28(1+0.06)17PV_0=\frac{FV}{{(1+0.06)}^{17}}=\frac{173,255.28}{{(1+0.06)}^{17}}PV0=(1+0.06)17FV=(1+0.06)17173,255.28PV0 = $64,340.85 ≈ $64,341. 第一步， PMT=50000，N=4,I/Y=6，FV=0，算出PV，用算出的PV值再乘以（1+I/Y），这个就是后面要求的值的FV第二步，用上面最终求得的值作为FV，PMT=0，N=18，I/Y=6，求PV这里第二步的N是不是就应该用18来算？
NO.PZ2017092702000014问题如下Granarents are funng a newborn’s future university tuition costs, estimate$50,000/yefor four years, with the first payment e a lump sum in 18 years. Assuming a 6% effective annurate, the requireposit toy is closest to:A.$60,699.B.$64,341.C.$68,201.B is correct. First, finthe present value (PV) of ornary annuity in Ye17 threpresents the tuition costs: 50,000[1−1(1+0.06)40.06]50,000{\lbrack\frac{1-\frac1{{(1+0.06)}^4}}{0.06}\rbrack}50,000[0.061−(1+0.06)41] = $50,000 × 3.4651 = $173,255.28. Then, finthe PV of the annuity in toy’s llars (where FV is future value):PV0=FV(1+0.06)17=173,255.28(1+0.06)17PV_0=\frac{FV}{{(1+0.06)}^{17}}=\frac{173,255.28}{{(1+0.06)}^{17}}PV0=(1+0.06)17FV=(1+0.06)17173,255.28PV0 = $64,340.85 ≈ $64,341.老师，学费不是都应该先付吗？这个不按照常识处理吗？另外，如果，18时点开始的payment 是先付，是不是答案就是C啊？，折到17年初，也就是16年末是173255。