Question

You are considering a 25-year, $1,000 par value bond. Its coupon rate is 10%, and interest is paid semiannually. If you require an "effective" annual interest rate (not a nominal rate) of 11.58%, how much should you be willing to pay for the bond? Do not round intermediate steps. Round your answer to the nearest cent.

Answer 1

	Periodic interest rate=	(1+Effective annual interest rate)^ 1/m -1
r=	effective annual interest rate	11.58%
m	number of periods	2
	Periodic interest rate=	(1+0.1158)^1/2    -1
	Semi-annual YTM	5.63143%

Now calculation of Bond price:

	Particulars	Cash flow	Discount factor	Discounted cash flow
	Interest payments-Annuity (5.631435%,50 periods)	50.0	16.6100	830.50
	Principle payments -Present value (5.631435%,50 periods)	1,000	0.0646	64.62
A	Bond price			895.12
	Face value			1,000.00
	Premium/(Discount)			-104.88
	Interest amount:
	Face value	1,000
	Coupon/stated Rate of interest	10.00%
	Frequency of payment(once in)	6 months
B	Interest amount	1000*0.1*6/12=		50
	Present value calculation:
	yield to maturity/Effective rate	11.26%
	Effective interest per period(i)	0.1126287*6/12=		5.631%
	Number of periods:
Ref	Particulars	Amount
a	Number of interest payments in a year	2
b	Years to maturiy	25.0
c=a*b	Number of periods	50