a). We can calculate the purchase price of the bond by using the following formula in excel:-

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

Here,

PV = Purchase price of the bond

Rate = 7%/2 = 3.5% (semiannual)

Nper = 10*2 = 20 periods (semiannual)

Pmt = Coupon payment = $100,000*3%/2 = $1,500

FV = $100,000

Substituting the values in formula:

= -pv(3.5%,20,1500,100000)

= $71,575.19

b). The bond is trading at discount because the coupon rate is less than the yield to maturity so the purchase price of the bond is lower than the face value.

Appropriate value = $100,000 - $71,575.19

= $28,424.81