关于Fixed income的两个问题请教

各位大神好，今天看到fixed income  equity 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！！！！！

第一个问题，题干中的4%指的本来就年利率，这也是为什么当转换成effective yield per 6-month period要除以2。如果要计算三个月的effective yield，只需要把六个月的yield开根号，也就是^0.5就可以了，当然你也可以把之前算出来的1.02的平方开四次方，结果是一样的。
第二个问题，当题目中说trade at 102，指的是face value的102%，题目中的face value是1000，所以issue price是1020。

1. 1.0404^0.25=1.00995, 再拿那个0.995% * 4= 3.98%; 建议如果不熟悉semi-annual直接换quarterly,monthly等，永远拿annual的换算，好理解也降低计算失误率

2. Face value 1000, 所以1020, 负号就是金融计算器要保证PMT,FV和PV符号相反

谢谢两位的解释，效率好高，我以为要沉了，都是很基本的问题，我也终于搞明白了，非常感谢！！！！