Assume that a 6 percent $500,000 bond with semiannual interest payments and a remaining life of 10 years could be purchased today, when market interest rates are 4.5 percent. How much would you have to pay to buy the bond?

I will pay $559,864 for this bond

Explanation:

Coupon payment = $500,000 x 6% = $30,000 annually  = $15,000 semiannually

Number of periods = 10 years x 2 = 20 period

Interest Rate = 4.5%  = 2.25% semiannually

Price of bond is the present value of future cash flows, to calculate Price of the bond use following formula:

Price of the Bond = C x [ ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]

Price of the Bond =$15,000 x [ ( 1 - ( 1 + 2.25% )^-20 ) / 2.25% ] + [ $1,000 / ( 1 + 2.25% )^20 ]

Price of the Bond = $15,000 x [ ( 1 - ( 1.0225 )^-20 ) / 0.0225 ] + [ $500,000 / ( 1.0225 )^20 ]

Price of the Bond = $239,455.68 + $320,408.24 = $559,863.92

Price of the Bond = $559,864

$530579.03

Explanation:

Bond Value Formula

BV = C×1-(1+r/m)^-nm/r/m + FV/(1+r/m)^nm

So we need to first calculate the semi annual coupon payment

given by C = C×FV/2

                   =0.06×$500000/2

                   =$15000

Then substitute into the formula for bond value

BV = 15000 × 1 -(1+0.045/2)^-10×2 /0.045/2+ 500000/(1+0.045/2)^10×2

      =$532579.03