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