Compute the price of a 3.8 percent coupon bond with 18 years left to maturity and a market interest rate of 7 percent. Compute the price again if interest payments are paid semi-annually (solve using semi-annual compounding). Par value is $1000. determine semi and annual compounding need both answers.

Answer:

Computation of Price of Bond (annual compounding) using PV Function in Excel:

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

Here,

PV = Price of Bond = ?

Rate = 7%

Nper = 18 Years 

PMT = $1,000*3.8% = $38

FV = $1,000

Substituting the values in formula:

=-pv(7%,18,38,1000)

PV or Price of Bond = $678.11

Computation of Price of Bond (semiannual compounding) using PV Function in Excel:

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

Here,

PV = Price of Bond = ?

Rate = 7%/2 = 3.5%

Nper = 18 Years * 2 = 36 Periods

PMT = $1,000*3.8%/2 = $19

FV = $1,000

Substituting the values in formula:

=-pv(3.5%,36,19,1000)

PV or Price of Bond = $675.35