Question

A $ 5000 bond with a coupon rate of 5.9​% paid semiannually has two years to maturity and a yield to maturity of 6.7​%. If interest rates fall and the yield to maturity decreases by​ 0.8%, what will happen to the price of the​ bond?

Answer 1

Duration:
Duaration = Sum [ Weight * Periods]

Period	CF	PVF @3.35%	Disc CF	Weight	Wt * Period
1	$    147.50	0.9676	$    142.72	0.0290	0.0290
2	$    147.50	0.9362	$    138.09	0.0280	0.0561
3	$    147.50	0.9059	$    133.62	0.0271	0.0814
4	$    147.50	0.8765	$    129.29	0.0262	0.1050
4	$ 5,000.00	0.8765	$ 4,382.56	0.8896	3.5585
Duration in Periods	3.8299
Periods per Year	2.0000
Duration in Years	1.9150

Modified duaration :
Modified duration = Duration / [ 1 + YTM ]
It specifies% change in Price in opposite direction due to 1% change in YTM.

= 1.915 / ( 1 + 0.067)

=1.915 / 1.067

= 1.79%

i.e 1% change in YTM leads to 1.79% change in price in opposite direction.

If YTM dec by 0.8%, Price will inc by 1.44% [ 1.79% * 0.8 ]

Pls do rate, if the answer is correct and comment, if any further assistance is required.