问题如下图：
选项：
A. 
B. 
C. 
解释：
why should use six years instead of three years?
发亮_品职助教 · 2018年05月31日
再求yield-to-first-call时，距现在有3年的时间，但是注意这三年中，每一年都有2期现金流，一共有6期现金流。因为题干是：with interest paid semiannually.
所以虽然是3年，但是要对6笔现金流折现，要折现6期。
第一期的现金流对应的折现率是1次方，第二期的现金流对应的折现率是平方，第三期的现金流对应的折现率是立方，直到第六期现金流对应的折现率是6次方。
这样算出来的r是每一期的收益率（即半年的收益率），要乘以2算出来Bond equivalent yield。这样才是题目要求的annual yield-to-first-call
另外还要注意最后一笔现金流包括一个call price，在第三年末是102。
NO.PZ2016031001000078 问题如下 A bonwith 5 years remaining until maturity is currently trang for 101 per 100 of pvalue. The bonoffers a 6% coupon rate with interest paisemiannually. The bonis first callable in 3 years, anis callable after thte on coupon tes accorng to the following schele: The bons annuyielto-first-call is closest to: A.3.12%. B.6.11%. C.6.25%. C is correct.The yielto-first-call is 6.25%. Given the first call te is exactly three years away, the formula for calculating this bons yielto-first-call is:PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+⋯+PMT(1+r)5+PMT+FV(1+r)6PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}+\cts+\frac{PMT}{{(1+r)}^5}+\frac{PMT+FV}{{(1+r)}^6}PV=(1+r)1PMT+(1+r)2PMT+(1+r)3PMT+⋯+(1+r)5PMT+(1+r)6PMT+FV101=3(1+r)1+3(1+r)2+3(1+r)3+⋯+3(1+r)5+3+102(1+r)6101=\frac3{{(1+r)}^1}+\frac3{{(1+r)}^2}+\frac3{{(1+r)}^3}+\cts+\frac3{{(1+r)}^5}+\frac{3+102}{{(1+r)}^6}101=(1+r)13+(1+r)23+(1+r)33+⋯+(1+r)53+(1+r)63+102r = 0.03123To arrive the annualizeyielto-first-call, the semiannurate of 3.123% must multiplietwo. Therefore, the yielto-first-call is equto 3.123% × 2 = 6.25% (roun. 考点YTC解析可利用计算器N=3×2=6，PMT=3，PV= -101，FV=102，算出来I/Y=3.12，再乘2得YTC=3.12×2=6.25%，故C正确。 N为什么等于6，一共不是5年期债券吗？
NO.PZ2016031001000078问题如下A bonwith 5 years remaining until maturity is currently trang for 101 per 100 of pvalue. The bonoffers a 6% coupon rate with interest paisemiannually. The bonis first callable in 3 years, anis callable after thte on coupon tes accorng to the following schele: The bons annuyielto-first-call is closest to:A.3.12%.B.6.11%.C.6.25%. C is correct.The yielto-first-call is 6.25%. Given the first call te is exactly three years away, the formula for calculating this bons yielto-first-call is:PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+⋯+PMT(1+r)5+PMT+FV(1+r)6PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}+\cts+\frac{PMT}{{(1+r)}^5}+\frac{PMT+FV}{{(1+r)}^6}PV=(1+r)1PMT+(1+r)2PMT+(1+r)3PMT+⋯+(1+r)5PMT+(1+r)6PMT+FV101=3(1+r)1+3(1+r)2+3(1+r)3+⋯+3(1+r)5+3+102(1+r)6101=\frac3{{(1+r)}^1}+\frac3{{(1+r)}^2}+\frac3{{(1+r)}^3}+\cts+\frac3{{(1+r)}^5}+\frac{3+102}{{(1+r)}^6}101=(1+r)13+(1+r)23+(1+r)33+⋯+(1+r)53+(1+r)63+102r = 0.03123To arrive the annualizeyielto-first-call, the semiannurate of 3.123% must multiplietwo. Therefore, the yielto-first-call is equto 3.123% × 2 = 6.25% (roun. 考点YTC解析可利用计算器N=3×2=6，PMT=3，PV= -101，FV=102，算出来I/Y=3.12，再乘2得YTC=3.12×2=6.25%，故C正确。 为什么这里coupon是3而不是3%乘PV
NO.PZ2016031001000078 问题如下 A bonwith 5 years remaining until maturity is currently trang for 101 per 100 of pvalue. The bonoffers a 6% coupon rate with interest paisemiannually. The bonis first callable in 3 years, anis callable after thte on coupon tes accorng to the following schele: The bons annuyielto-first-call is closest to: A.3.12%. B.6.11%. C.6.25%. C is correct.The yielto-first-call is 6.25%. Given the first call te is exactly three years away, the formula for calculating this bons yielto-first-call is:PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+⋯+PMT(1+r)5+PMT+FV(1+r)6PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}+\cts+\frac{PMT}{{(1+r)}^5}+\frac{PMT+FV}{{(1+r)}^6}PV=(1+r)1PMT+(1+r)2PMT+(1+r)3PMT+⋯+(1+r)5PMT+(1+r)6PMT+FV101=3(1+r)1+3(1+r)2+3(1+r)3+⋯+3(1+r)5+3+102(1+r)6101=\frac3{{(1+r)}^1}+\frac3{{(1+r)}^2}+\frac3{{(1+r)}^3}+\cts+\frac3{{(1+r)}^5}+\frac{3+102}{{(1+r)}^6}101=(1+r)13+(1+r)23+(1+r)33+⋯+(1+r)53+(1+r)63+102r = 0.03123To arrive the annualizeyielto-first-call, the semiannurate of 3.123% must multiplietwo. Therefore, the yielto-first-call is equto 3.123% × 2 = 6.25% (roun. 考点YTC解析可利用计算器N=3×2=6，PMT=3，PV= -101，FV=102，算出来I/Y=3.12，再乘2得YTC=3.12×2=6.25%，故C正确。 为什么pv不是100？
我用 N=10， PMT=3， Pv=-101 fv=102 算出来 I/y= 3.056 那里出错了？
老师你好，这道题目fist to call 的时候pv不是102嚒，谢谢解答