关于Fixed income的两个问题请教-经管之家官网！

各位大神好，今天看到fixed incomeequity valuation部分，其中2015版本notes当中P51页 关于adjusting yields for perodicity部分不是很理解，例题是这么说的：
An Atlas Corporation bond is quoted with a YTM of 4% on a semiannual bond basis. What yields should be used to compare it with a quarterly-pay bond and an annual-pay bond?
Answer:
The fisrt thing to note is that 4% on a seminanual bond basis is an effective yield of 2% per 6-month period.
To compare this with the yield on an annual-pay bond, which is an effective annual yeild, we need to calculate the effective annual yield on the semiannual coupon bond, which is 1.02平方-1=4.04%
到这一部分我没有问题，能理解。

For the annual YTM on the quarterly-paybond, we need to calculate the effective quarterly yield and multiply by four.The quarterly yield(yield per quarter)that is equivalent to a yield of 2% persix months is 1.02∧0.5-1=0.995%. The quoted annual rate for the equivalent yield on aquarterly bond basis is 4*0.995=3.98%.

我不理解的是为什么是0.5次方，为什么是0.5呢。我的思路是先把题干中半年付息一次的转化成一年付息的，为8%（年化），应该是（1+8/4%）4次方-1，但是这里是0.5次方，我怀疑我理解题目有问题是不是4%已经是年化了（至于多少频率付息一次另当别论），但是0.5我怎么也没法理解是怎么来的，谁除以谁？

第2个问题来自2015CFA level I notes 固收P53

Consider a 10-year, semiannual-pay 6% bond trading at 102 on Jannuary 1, 2014. The bond is callable according to the following schedule:

Callable at 102 on or after January 1, 2019.

Callable at 100 on or after January 1, 2022.

Calculate the bond's YTM, yield-to-first call, yield-to par call, and yield-to-worst.

Answer:

The yield-to maturity on the bond is calculated as:

N=20; PMT=30; FV=1000; PV=-1020; CPT----I/Y=2.867%

以上步骤计算器可以轻松算，那么问题来了，PV=-1020是怎么来的？别的数据我都能理解，PV想不明白。

请大神解释一下，谢谢了！！！！！

「经管之家」APP：经管人学习、答疑、交友，就上经管之家！
免流量费下载资料----在经管之家app可以下载论坛上的所有资源，并且不额外收取下载高峰期的论坛币。
涵盖所有经管领域的优秀内容----覆盖经济、管理、金融投资、计量统计、数据分析、国贸、财会等专业的学习宝库，各类资料应有尽有。
来自五湖四海的经管达人----已经有上千万的经管人来到这里，你可以找到任何学科方向、有共同话题的朋友。
经管之家（原人大经济论坛），跨越高校的围墙，带你走进经管知识的新世界。
扫描下方二维码下载并注册APP