1). Computation of the price of one bond:-

PV of interest payments = C*((1-1/(1+rate)^n)/rate)

Here,

C = Coupon payment = $1,000*3% = 30

PV of interest payments = $30*((1-1/(1+3.5%)^5)/3.5%)

= $30*4.515

= $135.45

PV of maturity amount = Face value / (1+rate)^n

= $1,000/(1+3.5%)^5

= $1,000/1.188

= $841.97

Present price of the bond = PV of interest payments + PV of maturity amount

= $135.45 + $841.97

= $977.42

The bond is selling on discount because the coupon rate is lower than the yield to maturity so the bond price is lower than the face value.

 

2). Computation of the selling price of bond:-

PV of interest payments = C*((1-1/(1+rate)^n)/rate)

Here,

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

C = Coupon payment = $1,000,000*8%/2= $40,000

n = (2019 - 2034)*2 = 30 periods semiannual)

PV of interest payments = $40,000*((1-1/(1+3.5%)^30)/3.5%)

= $40,000*18.392

= $735,681.82

PV of maturity amount = Face value / (1+rate)^n

= $1,000,000/(1+3.5%)^30

= $1,000,000/2.808

= $356,278.41

Present price of the bond = PV of interest payments + PV of maturity amount

= $735,681.82 + $356,278.41

= $1,091,960.23

The bond is selling at premium because the coupon rate is higher than the yield to maturity so the selling price is higher than the face value.

 

3). Computation of the selling price of bond:-

PV of interest payments = C*((1-1/(1+rate)^n)/rate)

Here,

n = (May 2019 to May 2029)*2 = 10*2 = 20 periods (semiannual)

Rate = 9%/2 = 4.5% (semiannual)

PV of interest payments = $50*((1-1/(1+4.5%)^20)/4.5%)

= $50*13.008

= $650.40

PV of maturity amount = Face value / (1+rate)^n

= $1,000/(1+4.5%)^20

= $1,000/2.412

= $414.64

Present price of the bond = PV of interest payments + PV of maturity amount

= $650.40 + $414.64

= $1,065.04

The bond is selling at premium because the coupon rate is higher than the yield to maturity so the selling price is higher than the face value.