Question

A $4,000 bond that has a coupon rate of 5.60% payable semi-annually and maturity of 7 years was purchased when the yield was 4.60% compounded semi-annually. What was the book value of the bond after 10 payments?

Answer 1

Book value of the bond after 10 payments was $ 4,075.60

Step-1:Calculation of price of bond
Price of bond is the present value of cash flows which is calculated as follows.
Price of bond		=	=-pv(rate,nper,pmt,fv)
		=	$ 4,237.09
Where,
rate	=	4.60%/2	=	0.023
nper	=	7*2	=	14
pmt	=	4000*5.60%*6/12	=	$     112.00
fv			=	$ 4,000.00
Step-2:Preparation of amortization schedule
Semi annual payment	Beginning book value	Interest expense	Coupon Payment	Premium amortization	Unamortized Premium	Ending Book Value
0					$      237.09	$ 4,237.09
1	$ 4,237.09	$    97.45	$     112.00	$       14.55	$      222.54	$ 4,222.54
2	$ 4,222.54	$    97.12	$     112.00	$       14.88	$      207.66	$ 4,207.66
3	$ 4,207.66	$    96.78	$     112.00	$       15.22	$      192.44	$ 4,192.44
4	$ 4,192.44	$    96.43	$     112.00	$       15.57	$      176.86	$ 4,176.86
5	$ 4,176.86	$    96.07	$     112.00	$       15.93	$      160.93	$ 4,160.93
6	$ 4,160.93	$    95.70	$     112.00	$       16.30	$      144.63	$ 4,144.63
7	$ 4,144.63	$    95.33	$     112.00	$       16.67	$      127.96	$ 4,127.96
8	$ 4,127.96	$    94.94	$     112.00	$       17.06	$      110.90	$ 4,110.90
9	$ 4,110.90	$    94.55	$     112.00	$       17.45	$         93.45	$ 4,093.45
10	$ 4,093.45	$    94.15	$     112.00	$       17.85	$         75.60	$ 4,075.60