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