A $ 5 comma 000 $5,000 bond with a coupon rate of 6.4 6.4% paid semiannually has ten ten years to maturity and a yield to maturity of 8.1 8.1%. If interest rates rise and the yield to maturity increases to 8.4 8.4%, what will happen to the price of the bond?

Price of the bond decreases by $92.60 or decreases by 2.09%

Explanation:

Semiannual coupon payment = 5,000 x 6.4%/2 = $160.

+ Price between yield to maturity changes ( YTM = 8.1%/2 = 4.05%):

Price of the bond = [ (160/0.0405) x ( 1 - 1.0405^-20) ] + 5,000/1.0405^20 = $4,424.96.

+ Price between yield to maturity changes ( YTM = 8.4%/2 = 4.2%):

Price of the bond = [ (160/0.042) x ( 1 - 1.042^-20) ] + 5,000/1.042^20 = $4,332.36.

=> Price of the bond decreases by $92.60 ( 4,332.36- 4,424.96) or decreases by 2.09% (4,332.36/4,424.96 - 1).

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