bond j has a coupon rate of 3 percent and bond k has a coupon rate of 9 percent. Both bonds have 13 years to maturity, make semiannual payments, and have a YTM of 6 percent. what if rates suddenly fall by 2 percent instesd?

if interest rates fall by 2%

price of bond j will increase to $756.83, price change = $756.83 - $663.28 = $93.55 or 14.1%

price of bond k will increase to $1,317.99, price change = $1,317.99 - $1,224.47 = $93.52 or 7.64%

Explanation:

bond j coupon rate 3%, 13 years to maturity, semiannual payments, YTM 6%

bond k coupon rate 9%, 13 years to maturity, semiannual payments, YTM 6%

current market price of bond j:

YTM = {coupon + [(face value - market value)/n]} / [(face value + market value)/2]

0.03 = {15 + [(1,000 - market value)/26]} / [(1,000 + market value)/2]

0.015(1,000 + market value) = 15 + [(1,000 - market value)/26]

15 + 0.015market value = 15 + 35.46 - 0.038market value

0.05346market value = 35.46

market value = 35.46 / 0.05346 = $663.28

current market price of bond k:

YTM = {coupon + [(face value - market value)/n]} / [(face value + market value)/2]

0.03 = {45 + [(1,000 - market value)/26]} / [(1,000 + market value)/2]

0.015(1,000 + market value) = 45 + [(1,000 - market value)/26]

15 + 0.015market value = 15 + 65.46 - 0.038market value

0.05346market value = 65.46

market value = 65.46 / 0.05346 = $1,224.47

if YTM decrease by 2%, then:

new market price of bond j:

0.02 = {15 + [(1,000 - market value)/26]} / [(1,000 + market value)/2]

0.01(1,000 + market value) = 15 + [(1,000 - market value)/26]

10 + 0.01market value = 15 + 35.46 - 0.038market value

0.05346market value = 40.46

market value = 40.46 / 0.05346 = $756.83

new market price of bond k:

YTM = {coupon + [(face value - market value)/n]} / [(face value + market value)/2]

0.02 = {45 + [(1,000 - market value)/26]} / [(1,000 + market value)/2]

0.01(1,000 + market value) = 45 + [(1,000 - market value)/26]

10 + 0.01market value = 15 + 65.46 - 0.038market value

0.05346market value = 70.46

market value = 70.46 / 0.05346 = $1,317.99

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