Question

​A(n) 13​-year bond has a coupon of 10​% and is priced to yield 9​%. Calculate the price per​ $1,000 par value using​ semi-annual compounding. If an investor purchases this bond two months before a scheduled coupon​ payment, how much accrued interest must be paid to the​ seller?

The price of the​ bond, PV​, is ​$

Answer 1

Years	N	Coupons	YTM @4.5%
	1	50	47.84689
1	2	50	45.7865
	3	50	43.81483
2	4	50	41.92807
	5	50	40.12255
3	6	50	38.39479
	7	50	36.74142
4	8	50	35.15926
	9	50	33.64522
5	10	50	32.19638
	11	50	30.80994
6	12	50	29.48319
	13	50	28.21358
7	14	50	26.99864
	15	50	25.83602
8	16	50	24.72347
	17	50	23.65882
9	18	50	22.64002
	19	50	21.66509
10	20	50	20.73214
	21	50	19.83937
11	22	50	18.98504
	23	50	18.16751
12	24	50	17.38517
	25	50	16.63653
13	26	1050	334.3226
			1075.733

Answer - Bond price - 1075.733

Now coupon payments are semi-annual. If bond is purchased 2 months before a coupon date

_______________________________

0 6m 10m 12m

the time between last coupon date (6m) and bond purchase date (10m) = 4 months

time between 2 coupon dates = 6 months

Coupon for 6 months are 10%*1000*1/2 = $50.

Hence, interest accrued to seller for 4 months = $50*4/6 = $33.33

Bond price at the date of bond purchase will be = Bond price at T=6months + accrued interest = 1074.14 + 33.33 = $1107.47