Question

Assume the effective interest method in accounting for these bonds. Build a 10 year amortization table.

Bond $650,000

Mature 10 years

State annual interest 9.25%

Effective annual rate 6%

Interest is paid every 6 months

Answer 1

Calculation of annualized YTM

	Periodic interest rate=	(1+Effective annual interest rate)^ 1/m -1
r=	effective annual interest rate	6%
m	number of payments	2
	Periodic interest rate=	(1+0.0617998195493841)^1/2    -1
	Periodic interest rate=	3.0437%
	Annualized	6.08734%

Bond price:

	Particulars	Cash flow	Discount factor	Discounted cash flow
	Interest payments-Annuity (3.04367%,20 periods)	30,062.5	14.8176	4,45,453.63
	Principle payments -Present value (3.04367%,20 periods)	6,50,000	0.5490	3,56,851.06
A	Bond price			8,02,304.69
	Face value			6,50,000.00
	Premium/(Discount)			1,52,304.69
	Interest amount:
	Face value	6,50,000
	Coupon/stated Rate of interest	9.25%
	Frequency of payment(once in)	6 months
B	Interest amount	650000*0.0925*6/12=		30062.5
	Present value calculation:
	yield to maturity/Effective rate	6.09%
	Effective interest per period(i)	0.0608734*6/12=		3.044%
	Number of periods:
Ref	Particulars	Amount
a	Number of interest payments in a year	2
b	Years to maturiy	10.0
c=a*b	Number of periods	20

Amortization schedule:

Period		Beginning carrying value	Interest expense	Interest paid	Premium amortisation	Ending carrying value	Balance premium
Year	Month end	A	C= A* 3.04%	D	E=C-D	F=A-E
1.00	6.00	8,02,304.69	24,419.51	30,062.50	5,642.99	7,96,661.69	1,46,661.69
1.00	12.00	7,96,661.69	24,247.75	30,062.50	5,814.75	7,90,846.95	1,40,846.95
2.00	6.00	7,90,846.95	24,070.77	30,062.50	5,991.73	7,84,855.22	1,34,855.22
2.00	12.00	7,84,855.22	23,888.40	30,062.50	6,174.10	7,78,681.12	1,28,681.12
3.00	6.00	7,78,681.12	23,700.48	30,062.50	6,362.02	7,72,319.11	1,22,319.11
3.00	12.00	7,72,319.11	23,506.84	30,062.50	6,555.66	7,65,763.45	1,15,763.45
4.00	6.00	7,65,763.45	23,307.31	30,062.50	6,755.19	7,59,008.26	1,09,008.26
4.00	12.00	7,59,008.26	23,101.71	30,062.50	6,960.79	7,52,047.47	1,02,047.47
5.00	6.00	7,52,047.47	22,889.84	30,062.50	7,172.66	7,44,874.81	94,874.81
5.00	12.00	7,44,874.81	22,671.53	30,062.50	7,390.97	7,37,483.84	87,483.84
6.00	6.00	7,37,483.84	22,446.57	30,062.50	7,615.93	7,29,867.92	79,867.92
6.00	12.00	7,29,867.92	22,214.77	30,062.50	7,847.73	7,22,020.19	72,020.19
7.00	6.00	7,22,020.19	21,975.91	30,062.50	8,086.59	7,13,933.60	63,933.60
7.00	12.00	7,13,933.60	21,729.78	30,062.50	8,332.72	7,05,600.88	55,600.88
8.00	6.00	7,05,600.88	21,476.16	30,062.50	8,586.34	6,97,014.55	47,014.55
8.00	12.00	6,97,014.55	21,214.82	30,062.50	8,847.68	6,88,166.87	38,166.87
9.00	6.00	6,88,166.87	20,945.53	30,062.50	9,116.97	6,79,049.90	29,049.90
9.00	12.00	6,79,049.90	20,668.04	30,062.50	9,394.46	6,69,655.44	19,655.44
10.00	6.00	6,69,655.44	20,382.10	30,062.50	9,680.40	6,59,975.04	9,975.04
10.00	12.00	6,59,975.04	20,087.46	30,062.50	9,975.04	6,50,000.00	-