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Olivia.W🌸 · 2024年07月23日

为什么不是full price=10/4/2014的PV+accrued interest?

  1. CFA I
  2. Fixed Income

NO.PZ2016031001000069

问题如下：

Bond G, described in the exhibit below, is sold for settlement on 16 June 2014.

Annual Coupon 5%

Coupon Payment Frequency Semiannual

Interest Payment Dates 10 April and 10 October

Maturity Date 10 October 2016

Day Count Convention 30/360

Annual Yield-to-Maturity 4%

The full price that Bond G will settle at on 16 June 2014 is closest to:

选项：

A.

102.36.

B.

103.10.

C.

103.65.

解释：

B is correct.

The bond’s full price is 103.10. The price is determined in the following manner:As of the beginning of the coupon period on 10 April 2014, there are 2.5 years (5semiannual periods) to maturity. These five semiannual periods occur on 10 October2014, 10 April 2015, 10 October 2015, 10 April 2016 and 10 October 2016.

PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+PMT(1+r)4+PMT+FV(1+r)5PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}+\frac{PMT}{{(1+r)}^4}+\frac{PMT+FV}{{(1+r)}^5}

PV=2.5(1+0.02)1+2.5(1+0.02)2+2.5(1+0.02)3+2.5(1+0.02)4+2.5+100(1+0.02)5PV=\frac{2.5}{{(1+0.02)}^1}+\frac{2.5}{{(1+0.02)}^2}+\frac{2.5}{{(1+0.02)}^3}+\frac{2.5}{{(1+0.02)}^4}+\frac{2.5\text{+}100}{{(1+0.02)}^5}

PV = 2.45 + 2.40 + 2.36 + 2.31 + 92.84 = 102.36

The accrued interest period is identified as 66/180. The number of days between10April2014 and 16 June 2014 is 66 days based on the 30/360 day count convention. (This is 20days remaining in April + 30 days in May + 16 days in June = 66 days total). The number of days between coupon periods is assumed to be 180 days using the 30/360 day convention.

PVFull=PV×(1 +r)66/180PV^{Full}=PV\times{(1\text{ }+r)}^{66/180}

PVFull= 102.36×(1.02)66/180= 103.10PV^{Full}=\text{ }102.36\times{(1.02)}^{66/180}=\text{ }103.10

考点：flat price & full price

解析：首先，我们将未来五笔现金流折现到2014.4.10，得到现值之和为102.36。N=5，PMT=2.5，I/Y=2，FV=100，求得PV=102.36

然后再将这个数值复利到2014.6.16，得到full price为103.10，故选项B正确。

我们之所以没有直接将未来五笔现金流折到2014.6.16，是因为五笔现金流的时间间隔不同，后面四笔现金流时间间隔是半年，而从6.16到10.10之间并不是半年。因此现金流就不是一个年金的形式，我们就没有办法用计算器直接求PV了。

为什么不是full price=10/4/2014的PV+accrued interest?

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1 个答案

品职答疑小助手雍 · 2024年07月24日

同学你好，这个是定义上的问题：

1、首先明确一点：102.36是4月10号的数值，这个数值既可以看成是full price，也可以看成是flat price（因为4.10是付息日，付息日当天的AI=0）。

2、如果102.36是6.16的flat price，才可以直接加上AI，即加上4.10到6.16之间的accrued intersect得到6.16的full price。时间点要对应好，不能拿着前一个时间点的flat price加上AI，得到这一时间的full price。

3、所以我们正确的思路是：将4.10的full price102.36复利到2014.6.16，得到full price为103.10。这两个数据都是full price，对应的时间点不同。

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NO.PZ2016031001000069 问题如下 BonG, scribein the exhibit below, is solfor settlement on 16 June 2014.AnnuCoupon 5%Coupon Payment Frequen SemiannualInterest Payment tes 10 April an10 OctoberMaturity te 10 October 2016y Count Convention 30/360AnnuYielto-Maturity 4%The full prithBonG will settle on 16 June 2014 is closest to: A.102.36. B.103.10. C.103.65. B is correct.The bons full priis 103.10. The priis terminein the following manner:of the beginning of the coupon perioon 10 April 2014, there are 2.5 years (5semiannuperio) to maturity. These five semiannuperio occur on 10 October2014, 10 April 2015, 10 October 2015, 10 April 2016 an10 October 2016. PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+PMT(1+r)4+PMT+FV(1+r)5PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}+\frac{PMT}{{(1+r)}^4}+\frac{PMT+FV}{{(1+r)}^5}PV=(1+r)1PMT​+(1+r)2PMT​+(1+r)3PMT​+(1+r)4PMT​+(1+r)5PMT+FV​PV=2.5(1+0.02)1+2.5(1+0.02)2+2.5(1+0.02)3+2.5(1+0.02)4+2.5+100(1+0.02)5PV=\frac{2.5}{{(1+0.02)}^1}+\frac{2.5}{{(1+0.02)}^2}+\frac{2.5}{{(1+0.02)}^3}+\frac{2.5}{{(1+0.02)}^4}+\frac{2.5\text{+}100}{{(1+0.02)}^5}PV=(1+0.02)12.5​+(1+0.02)22.5​+(1+0.02)32.5​+(1+0.02)42.5​+(1+0.02)52.5+100​PV = 2.45 + 2.40 + 2.36 + 2.31 + 92.84 = 102.36The accrueinterest periois intifie66/180. The number of ys between10April2014 an16 June 2014 is 66 ys baseon the 30/360 y count convention. (This is 20ys remaining in April + 30 ys in M+ 16 ys in June = 66 ys total). The number of ys between coupon perio is assumeto 180 ys using the 30/360 y convention.PVFull=PV×(1 +r)66/180PV^{Full}=PV\times{(1\text{ }+r)}^{66/180}PVFull=PV×(1 +r)66/180PVFull= 102.36×(1.02)66/180= 103.10PV^{Full}=\text{ }102.36\times{(1.02)}^{66/180}=\text{ }103.10PVFull= 102.36×(1.02)66/180= 103.10考点flpri full price解析首先，我们将未来五笔现金流折现到2014.4.10，得到现值之和为102.36。N=5，PMT=2.5，I/Y=2，FV=100，求得PV=102.36然后再将这个数值复利到2014.6.16，得到full price为103.10，故B正确。我们之所以没有直接将未来五笔现金流折到2014.6.16，是因为五笔现金流的时间间隔不同，后面四笔现金流时间间隔是半年，而从6.16到10.10之间并不是半年。因此现金流就不是一个年金的形式，我们就没有办法用计算器直接求PV了。 为什么要用半年期的利率来把4月10号的PV折算到6月16号。也就是， 为什么是用半年期对应的（1+2%）^(66/180)， 而不是用annual的数据， （1+4%）^(66/360)

2024-09-28 19:47 1 · 回答

NO.PZ2016031001000069 问题如下 BonG, scribein the exhibit below, is solfor settlement on 16 June 2014.AnnuCoupon 5%Coupon Payment Frequen SemiannualInterest Payment tes 10 April an10 OctoberMaturity te 10 October 2016y Count Convention 30/360AnnuYielto-Maturity 4%The full prithBonG will settle on 16 June 2014 is closest to: A.102.36. B.103.10. C.103.65. B is correct.The bons full priis 103.10. The priis terminein the following manner:of the beginning of the coupon perioon 10 April 2014, there are 2.5 years (5semiannuperio) to maturity. These five semiannuperio occur on 10 October2014, 10 April 2015, 10 October 2015, 10 April 2016 an10 October 2016. PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+PMT(1+r)4+PMT+FV(1+r)5PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}+\frac{PMT}{{(1+r)}^4}+\frac{PMT+FV}{{(1+r)}^5}PV=(1+r)1PMT​+(1+r)2PMT​+(1+r)3PMT​+(1+r)4PMT​+(1+r)5PMT+FV​PV=2.5(1+0.02)1+2.5(1+0.02)2+2.5(1+0.02)3+2.5(1+0.02)4+2.5+100(1+0.02)5PV=\frac{2.5}{{(1+0.02)}^1}+\frac{2.5}{{(1+0.02)}^2}+\frac{2.5}{{(1+0.02)}^3}+\frac{2.5}{{(1+0.02)}^4}+\frac{2.5\text{+}100}{{(1+0.02)}^5}PV=(1+0.02)12.5​+(1+0.02)22.5​+(1+0.02)32.5​+(1+0.02)42.5​+(1+0.02)52.5+100​PV = 2.45 + 2.40 + 2.36 + 2.31 + 92.84 = 102.36The accrueinterest periois intifie66/180. The number of ys between10April2014 an16 June 2014 is 66 ys baseon the 30/360 y count convention. (This is 20ys remaining in April + 30 ys in M+ 16 ys in June = 66 ys total). The number of ys between coupon perio is assumeto 180 ys using the 30/360 y convention.PVFull=PV×(1 +r)66/180PV^{Full}=PV\times{(1\text{ }+r)}^{66/180}PVFull=PV×(1 +r)66/180PVFull= 102.36×(1.02)66/180= 103.10PV^{Full}=\text{ }102.36\times{(1.02)}^{66/180}=\text{ }103.10PVFull= 102.36×(1.02)66/180= 103.10考点flpri full price解析首先，我们将未来五笔现金流折现到2014.4.10，得到现值之和为102.36。N=5，PMT=2.5，I/Y=2，FV=100，求得PV=102.36然后再将这个数值复利到2014.6.16，得到full price为103.10，故B正确。我们之所以没有直接将未来五笔现金流折到2014.6.16，是因为五笔现金流的时间间隔不同，后面四笔现金流时间间隔是半年，而从6.16到10.10之间并不是半年。因此现金流就不是一个年金的形式，我们就没有办法用计算器直接求PV了。 N=5，PMT=2.5，I/Y=2，FV=100，这种情况下如果把FV输入为-100，算出的PV就是78.789，请问是为什么？所以是否FV都是输入为正，PV输入都是为负，才可以得出正确结果？谢谢

2024-09-10 20:19 1 · 回答

NO.PZ2016031001000069问题如下BonG, scribein the exhibit below, is solfor settlement on 16 June 2014.AnnuCoupon 5%Coupon Payment Frequen SemiannualInterest Payment tes 10 April an10 OctoberMaturity te 10 October 2016y Count Convention 30/360AnnuYielto-Maturity 4%The full prithBonG will settle on 16 June 2014 is closest to:A.102.36.B.103.10.C.103.65. B is correct.The bons full priis 103.10. The priis terminein the following manner:of the beginning of the coupon perioon 10 April 2014, there are 2.5 years (5semiannuperio) to maturity. These five semiannuperio occur on 10 October2014, 10 April 2015, 10 October 2015, 10 April 2016 an10 October 2016. PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+PMT(1+r)4+PMT+FV(1+r)5PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}+\frac{PMT}{{(1+r)}^4}+\frac{PMT+FV}{{(1+r)}^5}PV=(1+r)1PMT​+(1+r)2PMT​+(1+r)3PMT​+(1+r)4PMT​+(1+r)5PMT+FV​PV=2.5(1+0.02)1+2.5(1+0.02)2+2.5(1+0.02)3+2.5(1+0.02)4+2.5+100(1+0.02)5PV=\frac{2.5}{{(1+0.02)}^1}+\frac{2.5}{{(1+0.02)}^2}+\frac{2.5}{{(1+0.02)}^3}+\frac{2.5}{{(1+0.02)}^4}+\frac{2.5\text{+}100}{{(1+0.02)}^5}PV=(1+0.02)12.5​+(1+0.02)22.5​+(1+0.02)32.5​+(1+0.02)42.5​+(1+0.02)52.5+100​PV = 2.45 + 2.40 + 2.36 + 2.31 + 92.84 = 102.36The accrueinterest periois intifie66/180. The number of ys between10April2014 an16 June 2014 is 66 ys baseon the 30/360 y count convention. (This is 20ys remaining in April + 30 ys in M+ 16 ys in June = 66 ys total). The number of ys between coupon perio is assumeto 180 ys using the 30/360 y convention.PVFull=PV×(1 +r)66/180PV^{Full}=PV\times{(1\text{ }+r)}^{66/180}PVFull=PV×(1 +r)66/180PVFull= 102.36×(1.02)66/180= 103.10PV^{Full}=\text{ }102.36\times{(1.02)}^{66/180}=\text{ }103.10PVFull= 102.36×(1.02)66/180= 103.10考点flpri full price解析首先，我们将未来五笔现金流折现到2014.4.10，得到现值之和为102.36。N=5，PMT=2.5，I/Y=2，FV=100，求得PV=102.36然后再将这个数值复利到2014.6.16，得到full price为103.10，故B正确。我们之所以没有直接将未来五笔现金流折到2014.6.16，是因为五笔现金流的时间间隔不同，后面四笔现金流时间间隔是半年，而从6.16到10.10之间并不是半年。因此现金流就不是一个年金的形式，我们就没有办法用计算器直接求PV了。 最后为什么不是102。36 x （1+4%）的66/360次方？

2024-08-10 22:46 2 · 回答

NO.PZ2016031001000069 问题如下 BonG, scribein the exhibit below, is solfor settlement on 16 June 2014.AnnuCoupon 5%Coupon Payment Frequen SemiannualInterest Payment tes 10 April an10 OctoberMaturity te 10 October 2016y Count Convention 30/360AnnuYielto-Maturity 4%The full prithBonG will settle on 16 June 2014 is closest to: A.102.36. B.103.10. C.103.65. B is correct.The bons full priis 103.10. The priis terminein the following manner:of the beginning of the coupon perioon 10 April 2014, there are 2.5 years (5semiannuperio) to maturity. These five semiannuperio occur on 10 October2014, 10 April 2015, 10 October 2015, 10 April 2016 an10 October 2016. PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+PMT(1+r)4+PMT+FV(1+r)5PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}+\frac{PMT}{{(1+r)}^4}+\frac{PMT+FV}{{(1+r)}^5}PV=(1+r)1PMT​+(1+r)2PMT​+(1+r)3PMT​+(1+r)4PMT​+(1+r)5PMT+FV​PV=2.5(1+0.02)1+2.5(1+0.02)2+2.5(1+0.02)3+2.5(1+0.02)4+2.5+100(1+0.02)5PV=\frac{2.5}{{(1+0.02)}^1}+\frac{2.5}{{(1+0.02)}^2}+\frac{2.5}{{(1+0.02)}^3}+\frac{2.5}{{(1+0.02)}^4}+\frac{2.5\text{+}100}{{(1+0.02)}^5}PV=(1+0.02)12.5​+(1+0.02)22.5​+(1+0.02)32.5​+(1+0.02)42.5​+(1+0.02)52.5+100​PV = 2.45 + 2.40 + 2.36 + 2.31 + 92.84 = 102.36The accrueinterest periois intifie66/180. The number of ys between10April2014 an16 June 2014 is 66 ys baseon the 30/360 y count convention. (This is 20ys remaining in April + 30 ys in M+ 16 ys in June = 66 ys total). The number of ys between coupon perio is assumeto 180 ys using the 30/360 y convention.PVFull=PV×(1 +r)66/180PV^{Full}=PV\times{(1\text{ }+r)}^{66/180}PVFull=PV×(1 +r)66/180PVFull= 102.36×(1.02)66/180= 103.10PV^{Full}=\text{ }102.36\times{(1.02)}^{66/180}=\text{ }103.10PVFull= 102.36×(1.02)66/180= 103.10考点flpri full price解析首先，我们将未来五笔现金流折现到2014.4.10，得到现值之和为102.36。N=5，PMT=2.5，I/Y=2，FV=100，求得PV=102.36然后再将这个数值复利到2014.6.16，得到full price为103.10，故B正确。我们之所以没有直接将未来五笔现金流折到2014.6.16，是因为五笔现金流的时间间隔不同，后面四笔现金流时间间隔是半年，而从6.16到10.10之间并不是半年。因此现金流就不是一个年金的形式，我们就没有办法用计算器直接求PV了。 我好像跟什么题目搞混了，有道题是再投资的，什么时候才会再投资来着？

2024-07-23 21:24 2 · 回答