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On September 1, 2013 Thomas Doniphon purchased a U.S. Government bond having a coupon rate of 4.5 percent, a par value of $1000 and 20 years to maturity.                    Assuming that the bond makes semiannual coupon payments and is priced to offer investors a semiannually compounded yield to maturity of 5.0 percent.

                    a. determine the price of the bond on September 1, 2013

                    b. if the required yield to maturity for the bond increases to 6.0 percent on September 28, 2013 and then remains constant, so that future coupon payments will                    be reinvested at 6.0 percent compounded semiannually, determine the future amount to which the initial investment will have grown by September 1, 2033 when the                    bond matures.

Explanation / Answer

a. Coupon 4.5% Semi, Par Value = FV =1000

Coupon PMT = 4.5%*1000/2 = $22.50

nper = 20*2 = 40 periods

Semiannual YTM = Rate = 5%/2

So Price of Bond = PV(Rate,nper,pmt,fv)

= PV(5%/2,40,-22.50,1000)

= -$937.24 ............>Ans (a)

b. New YTM = 6%

PMT = 22.50

nper =40

Present value of COupon pmts = 0

SO Future value of coupon payments = FV(rate,nper,PMT,PV)

= FV(6%/2,40,-22.50,0)

= $1,696.53

Also Par value will be returned on Maturity = $1000

SO Initil Inv of $937.24 will grow to $1,696.53+$1000 = $2,696.53 in 20 Yrs

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