Question

I have two bonds which Bond 1 pays annually and Bond 2 pays semi Annually( manually calculation not excell)

Bond 1:YTM=3.50%,Coupon value = 5.25%,maturity in years is 20

Bond 2:YTM=5.25%,Coupon value = 3.75%,maturity in years is 6

Face value is $100

calculate the prices of 2 Bonds

show formula as well

Answer 1

Price of Bonds

Price of the bond=present value of coupon bond for n years+PV of maturity value

                        =C/(1+i)+C/(1+i)²⁺C(1+i)³……..C(1+i)ⁿ+M/(1+i)ⁿ

Where i=yield to maturity

C=coupon value

M=maturity value

Using formula for finding sum of G.P(a*(1-rⁿ⁾/(1-r)), we get

Price of bond=C*{1-(1/(1+i)ⁿ)}/i +M/(1+i)ⁿ

Price of bond 1

Price of bond= C*{1-(1/(1+i)ⁿ)}/i +M/(1+i)ⁿ

                             =100*5.25/100*{1-(1/1.035)²⁰}/3.5%+100/(1.035)²⁰

                            =5.25*(1-0.966184²⁰)/3.5%+100/1.989783

                         =5.25*(1-0.50257)/3.5%+50.25659

                      =5.25*0.49743/3.5%+50.25659

                        =5.25*14.21228+50.25659

                        =$74.615+50.257

                         =$124.871

Price of bond 2

Price of semi annual bond= C/2*{1-(1/(1+i/2)²ⁿ)}/i +M/(1+i/2)²ⁿ

                       =3.75/2*{1-(1/1.02625)^6*2}/2.625%+100/(1.02625)¹²

                            =1.875*(1-0.974421¹²)/2.625%+100/1.36471

                         =1.875*(1-0.732756)/2.625%+73.27564

                      =1.875*0.267244/2.625%+73.2564

                        =1.875*10.18071+73.27564

                      =19.08883+73.27564=$92.36