Question

Assume the current Treasury yield curve shows that the spot rates for six​ months, one​ year, and one and a half years are 1%, 1.1%​, and ​1.3%, all quoted as semiannually compounded APRs.

What is the price of a ​$1000 ​par, 5% coupon bond maturing in one and a half years​ (the next coupon is exactly six months from​ now)

Answer 1

Given the following information,

term in years	r
0.5	0.01
1.0	0.011
1.5	0.013

Face value = 1000

Coupon rate = 5% = 0.05

Number of coupon payments in a year = semiannual = 2

Coupon payment = Coupon rate*face value/ Number of coupon payments in a year

Coupon payment CPN = 0.05*1000/ 2 = 50/2 = 25

Price of the bond is given by the following formula,

P = PV(Bond cash flows)

Since given semiannually compounded Annual percentage rates,

P = CPN/(1+r1/2)^1 + CPN/(1+r2/2)^2 + (CPN+FV)/(1+r3/2)^3

P = 25/(1+0.01/2)^1 + 25/(1+0.011/2)^2 + (25+1000)/(1+0.013/2)^3

P = 25/(1+0.0050)^1 + 25/(1+0.0055)^2 + (25+1000)/(1+0.0065)^3

P = 25/(1.0050)^1 + 25/(1.0055)^2 + (1025)/(1.0065)^3

P = 25/(1.0050) + 25/1.0110 + 1025/1.0196

P = 24.88 + 24.73 + 1005.27

P = 1054.87

Therefore, the price of the bond is $1054.87