Question

A bond face value is $1000, with a 6-year maturity. Its annual coupon rate is 7% and issuer makes semi-annual coupon payments. The annual yield of maturity for the bond is 6%. The bond was issued on 7/1/2017. An investor bought it on 8/1/2019. Calculate its dirty price, accrued interests, and clean price.

Answer 1

Let us find the clean Price of Bond as on 8/1/2019
Par value of Bond	$       1,000.00
Semi annual coupon @7% pa=	$             35.00
Remaining maturity period on 07/1/2019 =4 years
Remaining Coupon payments due =8 nos
YTM =6%
Semi annual YTM =3%
PVIF Factor @3% for 8 period =(1-1.03^-8)/3% =	7.0197
PV factor @3% for 8 period =1/1.03^8=	0.7894

Finding the Bond Price from the PV of Cash flows
Cash flows	Amt $	PVIF /PV factor	PV of Cash flows
Coupon payment for 8 periods	$                  35	7.0197	$          245.69
Maturity Value	$             1,000	0.7894	$          789.41
Total of PV of Cash flows			$      1,035.10

So Clean Price of Bond =$1,035.10
Accumulated Interest till 8/1/2019=1000*7%*1/12=	$               5.83
So Dirty Price with accrued interest on 8/19/19=	$       1,040.93