Answer:
$ 73.66
Explanation:
The initial price is derived using the pv formula in excel as below:
=-pv(rate,nper,pmt,fv)
rate is the yield to maturity of 4.25% divided by 2 i.e =2.125%
nper is the number of coupons the bond would pay which 8 years multiplied by 2 i.e 16
pmt is the semiannual coupon=$1000*7.75%*6/12=$38.75
fv is the face value of $1000
=-pv(2.125%,16,38.75,1000)=$ 1,235.27
1% increase in yield to maturity:
=-pv(5.25%/2,16,38.75,1000)=$ 1,161.61
The price would fall to $ 1,161.61 if interest rate rises by 1%
Change in bond's price=$ 1,235.27-$ 1,161.61 =$ 73.66
