A $ 5000 bond with a coupon rate of 6.7% paid semiannually has eight years to maturity and a yield to maturity of 7.8%. If interest rates rise and the yield to maturity increases to 8.1%, what will happen to the price of the bond?

As a result of an increase in the YTM, the price of the bond will fall $4677.19 from to $4593.67

Explanation:

The bonds are valued or priced based on the present value of annuity of interest payments and the present value of the principal. Based on the YTM of 7.8% the bonds are priced at,

coupon payment = 5000 * 0.067 *1/2  =  $167.5

Semiannual YTM = 7.8 *0.5  =  3.9%

Semi annual periods to maturity = 8 * 2  =  16 periods

Old Price = 167.5 * [( 1 - (1 + 0.039)^-16  + 5000 / (1+0.039)^16

Old Price = $4677.19

New semiannual YTM = 8.1% / 2  =  4.05%

New Price = 167.5 * [( 1 - (1+0.0405)^-16) / 0.0405] + 5000 / 1.0405^16

New Price = $4593.67