ciaoyy · 2017年12月18日
问题如下图：
选项：
A. 
B. 
C. 
解释：
1. 题目中的 in 18 years指的是18年年末还是年初呢？我认为指的是年末，即从0开始的刻度线，过了18年，对应的应该是18刻度线。
2. 大学每年年初付学费，为什么是annuity due呢？
3. 算1st PMT的PV时，为什么N=17，不等于18？题目不是问‘today‘s deposit’吗？从18刻度线到0刻度线，应该折现了18次才对(annuity due)？
按照上述疑问重做题目，发现答案一致:
1.求18年初PV。 BEG: N=4, PMT=-50K, I/Y=6, FV=0
2.求0时刻1st PMT的PV。BEG: N=18, PMT=0, I/Y=6, FV=上面的pv
是巧合吗？
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。
