Question

what are the price and duration of 5 year , 7% coupon, semi-annual bond if market interest rate is 4%

Answer 1

Price = PV of CFs from it.

Assuming 1000 is Face Value.

Period	CF	PVF @2%	Disc CF
1	$      35.00	0.9804	$      34.31
2	$      35.00	0.9612	$      33.64
3	$      35.00	0.9423	$      32.98
4	$      35.00	0.9238	$      32.33
5	$      35.00	0.9057	$      31.70
6	$      35.00	0.8880	$      31.08
7	$      35.00	0.8706	$      30.47
8	$      35.00	0.8535	$      29.87
9	$      35.00	0.8368	$      29.29
10	$      35.00	0.8203	$      28.71
10	$ 1,000.00	0.8203	$    820.35
Price of Bond			$ 1,134.74

Duration = Sum(Weight * year)

Period	CF	PVF @2%	Disc CF	Weight	Duration
1	$      35.00	0.9804	$      34.31	0.0302	0.0302
2	$      35.00	0.9612	$      33.64	0.0296	0.0593
3	$      35.00	0.9423	$      32.98	0.0291	0.0872
4	$      35.00	0.9238	$      32.33	0.0285	0.1140
5	$      35.00	0.9057	$      31.70	0.0279	0.1397
6	$      35.00	0.8880	$      31.08	0.0274	0.1643
7	$      35.00	0.8706	$      30.47	0.0269	0.1880
8	$      35.00	0.8535	$      29.87	0.0263	0.2106
9	$      35.00	0.8368	$      29.29	0.0258	0.2323
10	$      35.00	0.8203	$      28.71	0.0253	0.2530
10	$ 1,000.00	0.8203	$    820.35	0.7229	7.2294
Duration in Periods					8.7080

Duration = 8.71 Periods

Duration in Years = Duration / Periods in Year

= 8.71 / 2

= 4.35 Years.