Question

A $5,000 bond with a coupon rate of 6.4% paid semi-annually has four years to maturity and a yield to maturity of 6.2%. If interest rates fall and the yield to maturity decreases by 0.8%, what will happen to the price of the bond?

	a.	Fall by $40.49.
	b.	Rise by $142.78.
	c.	Rise by $84.46.
	d.	Fall by $98.64.
	e.	None of the answers are correct.

Answer 1

Answer)

Given

Interest Rate	= 6.2% / 2 = 3.1%
Coupon	= (0.064 X 5000) / 2 =$160
n	= 4 X 2 = 8 YEARS

Price = Coupon x [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Price = 160 x [ 1 - 1 / (1.031)⁸] / 0.031 + 5000 / (1 + 0.031)⁸

= 160 x 6.85 + 3937

= $5035

Interest Rate	= 6.2% - 0.8% = 5.4%
Coupon	= (0.064 X 5000) / 2 =$160
n	= 4 X 2 = 8 YEARS
Rate	= 5.4% / 2 = 2.7%

Price = Coupon x [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Price = 160 x [ 1 - 1 / (1.027)⁸] / 0.0327 + 5000 / (1 + 0.027)⁸

= 160 x 7.09 + 4042

= $ 5177

Change in price = $5177 - $5035

= $142

Price has fallen by $142.