Question

9- An 8% coupon rate $1,000 bond matures in 10 years, pays interest semi-annually, and has a yield to maturity of 5.5%. What is the current market price of the bond?______

	A-	$889.35
	B-	$1,000
	C-	$1,190.34
	D-	$993.62

10- If you earned a rate of return of 8% on your bond investments last year. During that time the inflation rate was 2.68%. What is your real rate of return?

A-		3.98%
B-		4.57%
C-		4.72%
D-		5.18%

Answer 1

Solution:
9.	Answer is C. $1,190.34
Working Notes:
	Bond Price = Periodic Coupon Payments x Cumulative PVF @ periodic YTM (for t= to t=n) + PVF for t=n @ periodic YTM x Face value of Bond
	Coupon Rate = 8%
	Annual coupon = Face value of bond x Coupon Rate = 1,000 x 8 % = $80
	Semi annual coupon = Annual coupon / 2 = $80/2=$40
	YTM= 5.50% p.a (annual)
	Semi annual YTM= 5.50%/2 = 2.75%
	n= no.of coupon = No. Of years x no. Of coupon in a year
	= 10 x 2 = 20
	Bond Price = Periodic Coupon Payments x Cumulative PVF @ periodic YTM (for t= to t=n) + PVF for t=n @ periodic YTM x Face value of Bond
	= $ 40 x Cumulative PVF @ 2.75% for 1 to 20th + PVF @ 2.75% for 20th period x 1,000
	= 40 x 15.22725213 + 1000 x0.581250566
	=$1,190.34
Cumulative PVF @ 2.75% for 1 to 20th is calculated = (1 - (1/(1 + 0.0275)^20) ) /0.0275 = 15.22725213
	PVF @ 2.75% for 20th period is calculated by = 1/(1+i)^n = 1/(1.0275)^20 =0.581250566
10.	Answer is D. 5.18%
Working Notes:
	As per Fisher effect
	(1+ real rate) (1+inflation) = (1+ nominal rate of interest)
	(1+ r) (1+ 0.0268) = (1 + 0.08)
	r= 0.05181145
	r = 5.18%
	Real rate of return r = 5.18%
Please feel free to ask if anything about above solution in comment section of the question.