A 20-year 10% semi-annual-coupon bond has a face (and redemption) value of $1,000. Find the price...

A 20-year 10% semi-annual-coupon bond has a face (and redemption) value of $1,000. Find the price of the bond, assuming a nominal annual interest rate of 12% convertible semiannually

[I am not good at this class so a thorough write out on paper would be most beneficial to me]

Answer: 849.54 [Provided on the homework, but i don't know how to solve]

Solutions

Expert Solution

Period	Discounting Factor [1/(1.06^period)]	Discounting Factor Annuity (Sum of discounting factor & all previous discounting factors)
1	0.943396226	0.943396226
2	0.88999644	1.833392666
3	0.839619283	2.673011949
4	0.792093663	3.465105613
5	0.747258173	4.212363786
6	0.70496054	4.917324326
7	0.665057114	5.58238144
8	0.627412371	6.209793811
9	0.591898464	6.801692274
10	0.558394777	7.360087051
11	0.526787525	7.886874577
12	0.496969364	8.38384394
13	0.468839022	8.852682963
14	0.442300964	9.294983927
15	0.417265061	9.712248988
16	0.393646284	10.10589527
17	0.371364419	10.47725969
18	0.350343791	10.82760348
19	0.33051301	11.15811649
20	0.311804727	11.46992122
21	0.294155403	11.76407662
22	0.277505097	12.04158172
23	0.261797261	12.30337898
24	0.246978548	12.55035753
25	0.232998631	12.78335616
26	0.219810029	13.00316619
27	0.207367952	13.21053414
28	0.195630143	13.40616428
29	0.184556739	13.59072102
30	0.174110131	13.76483115
31	0.16425484	13.92908599
32	0.154957397	14.08404339
33	0.146186223	14.23022961
34	0.137911531	14.36814114
35	0.130105218	14.49824636
36	0.122740772	14.62098713
37	0.115793181	14.73678031
38	0.10923885	14.84601916
39	0.103055519	14.94907468
40	0.097222188	15.04629687

Coupons pending = Time till maturity = 20 years = 20*2(because smi-annually) = 40 Coupons

Price of Bond = PV of All Coupons + PV of Maturity Value

= [Coupon*Annuity Factor] + [Maturity Value*Discounting Factor]

= [1000*5%*15.04629687] + [1000*0.097222188] = 752.3148 + 97.222 = $849.5368 = $849.54

jeff jeffy answered 1 year ago

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