Question

Assume the current Treasury yield curve shows that the spot rates 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 $1,000 par, 5% coupon bond maturing in one and a half year s (the next coupon is exactly 6 months from now)?

Answer 1

6 month interest rate is 1% p.a

rate for semiannual period (i1) = 1%/2 = 0.5%

1 year interest rate is 1.1%

rate for semainnaul period (i2)= 1.1%/2 =0.55%

1 and half year interest rate = 1.3%

rate for semainnaul period (i3)= 1.3%/2 =0.65%

Calculaiton of price of bond:

face value = 1000

coupon paid semiannual = face value*coupon rate/2

=1000*5%/2 = 25

Price of bond is present value of interest and maturity value received.

Price of bond formula = (Coupon/(1+i1)^1) +(Coupon/(1+i2)^2) + ((Coupon+matuirty value)/(1+i3)^3)

=(25/(1+0.5%)^1) + (25/(1+0.55%)^2) + ((25+1000)/(1+0.65%)^3)

=1054.872424

so bond price is $1054.87