A $1000 bond with a coupon rate of 6.2% paid semiannually has eight years to maturity and a yield to maturity of 8.3%. If interest rates rise and the yield to maturity increases to 8.6%, what will happen to the price of the bond

The price of the bond will be $879

Explanation:

Price of the bond is the present value of all cash flows of the bond. Price of the bond is calculated by following formula:

According to given data

Coupon payment = C = $1,000 x 6.2 = $62 annually = $31 semiannually

Number of periods = n = 2 x 8 years = 16 periods

Current Yield = r = 8.3% / 2  = 4.15% semiannually

Price of the Bond = $31 x [ ( 1 - ( 1 + 4.15% )^-16 ) / 4.15% ] + [ $1,000 / ( 1 + 4.15% )^16 ]

Price of the Bond = $31 x [ ( 1 - ( 1 + 0.0415)^-16 ) / 0.0415 ] + [ $1,000 / ( 1 + 0.0415 )^16 ]  

Price of the Bond = $31 x [ ( 1 - ( 1.0415)^-16 ) / 0.0415 ] + [ $1,000 / ( 1.0415 )^16 ]  

Price of the Bond = $521.74 + $357.26   = $879