We can calculate the price of one bond by using the following formula in excel:-

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

Here,

PV = Price of one bond

Rate = 4%

Nper = 3 periods

Pmt = 0

FV = 1000

Substituting the values in formula:

= -pv(4%,3,0,1000)

= 889

 

We can calculate the rate on second bond by using the following formula in excel:-

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

Here,

Rate = Rate on second bond (semiannual)

Nper = 6*2 = 12 periods (semiannual)

Pmt = Coupon payment = 1000*6%/2 = 30

PV = 889

FV = 1000

Substituting the values in formula:

= rate(12,30,-889,1000)

= 4.20%

Effective yield = (1+Semi annual yield)^n-1

= (1+4.20%)^2-1

= 1.0857 - 1

= 8.57%