Compute the price of a 3.8 percent coupon bond with 18 years left to maturity and a market interest rate of 7 percent

Assume interest payments are paid semi-annually and solve using semi-annual compounding.

Computation of the price of the bond:-

Price of the bond = (Coupon payment * ((1 - 1 / ( 1 + r)^n) / r)) + (FV / ( 1 + r)^n)

Coupon payment = $1,000*3.8%/2 = $19

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

n = 18*2 = 36 periods (semiannual)

Substituting the values in formula:

Price of the bond = ($19*((1-1/(1+3.5%)^36)/3.5%)) + ($1,000/(1+3.5%)^36)

= ($19*20.2905) + ($1,000/3.4503)

= $385.52 + $289.83

= $675.35