Bond J has a coupon rate of 5 percent and Bond K has a coupon rate of 11 percent. Both bonds have 14 years to maturity, make semiannual payments, and have a YTM of 8 percent. a. If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds?

Bond J - 16.33%

Bond K - 14.04%

Explanation:

In order to determine the percentage price change it is incumbent to establish the bonds' prices with YTM of 8% as well as when interest rises by 2% so as to calculate the price change percentage.

The pv formula can be used to establish the prices as follows:

=-pv (rate, nper, pmt, fv)

rate is semiannual yield to maturity of both bonds which 8%/2=4%

nper is the number of coupon interest payable by the bonds which 14 years multiplied by 2 i. e 28

pmt is the semiannual coupon payment by the bonds:

Bond J=$1000*5%/2=$25

Bond K=$1000*11%/2=$55

fv is the face of the bonds which is $1000 in both cases

Price of bond J;

=-pv (4%,28,25,1000) = $ 750.05

Price of Bond K:

=-pv (4%,28,55,1000) = $1,249.95

New price with 2% increase in interest

Yield previously 8%

plus increase 2%'

total 10%

divided by 2=10%/2=5%

Price of bond J;

=-pv (5%,28,25,1000) = $627.55

Price of Bond K:

=-pv (5%,28,55,1000) = $ 1,074.49

Change in price=new price-old price/old price

Bond J = ($627.55-$ 750.05) / $ 750.05=-16.33%

Bonk K = ($1,074.49-$1,249.95) / $1,249.95 = -14.04%