Question

You are considering a 15-year, $1,000 par value bond. Its coupon rate is 8%, and interest is paid semiannually. If you require an "effective" annual interest rate (not a nominal rate) of 7.6420%, how much should you be willing to pay for the bond? Do not round intermediate calculations. Round your answer to the nearest cent.

$________

Answer 1

EAR = (1+r)^n - 1

0.076420 = ( 1+r)^2 - 1

1+0.076420 = (1+r)^2

(1+r)^2 = 1.076420

1+r = 1.076420^ (1/2)

= 1.0375

r = 1.0375 - 1

= 0.0375 i.e 3.75%

Int rate is 3.75% per six months.

Price of Bond is pV of CFs from it.

Period	CF	PVF @3.75%	Disc CF
1	$      40.00	0.9639	$      38.55
2	$      40.00	0.9290	$      37.16
3	$      40.00	0.8954	$      35.82
4	$      40.00	0.8631	$      34.52
5	$      40.00	0.8319	$      33.28
6	$      40.00	0.8018	$      32.07
7	$      40.00	0.7728	$      30.91
8	$      40.00	0.7449	$      29.80
9	$      40.00	0.7180	$      28.72
10	$      40.00	0.6920	$      27.68
11	$      40.00	0.6670	$      26.68
12	$      40.00	0.6429	$      25.72
13	$      40.00	0.6197	$      24.79
14	$      40.00	0.5973	$      23.89
15	$      40.00	0.5757	$      23.03
16	$      40.00	0.5549	$      22.19
17	$      40.00	0.5348	$      21.39
18	$      40.00	0.5155	$      20.62
19	$      40.00	0.4969	$      19.87
20	$      40.00	0.4789	$      19.16
21	$      40.00	0.4616	$      18.46
22	$      40.00	0.4449	$      17.80
23	$      40.00	0.4288	$      17.15
24	$      40.00	0.4133	$      16.53
25	$      40.00	0.3984	$      15.94
26	$      40.00	0.3840	$      15.36
27	$      40.00	0.3701	$      14.80
28	$      40.00	0.3567	$      14.27
29	$      40.00	0.3438	$      13.75
30	$      40.00	0.3314	$      13.26
30	$ 1,000.00	0.3314	$    331.40
Price of Bond			$ 1,044.57

Price of Bond is $ 1,044.57