Question

You find the following Treasury bond quotes. To calculate the number of years until maturity, assume that it is currently May 2019 and the bond has a par value of $1,000.

Rate	Maturity Mo/Yr	Bid	Asked	Chg	Ask Yld
??	May 24	103.5540	103.5418	+.3093	6.119
5.524	May 29	104.5030	104.6487	+.4365	??
6.193	May 39	??	??	+.5483	4.151

a.	In the above table, find the Treasury bond that matures in May 2039. What is the asked price of this bond in dollars? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	If the bid-ask spread for this bond is .0566, what is the bid price in dollars? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Par Value (in $) = $1000.00

Treasury bonds pay Coupon Semiannually. So yield and coupon will be calculated for Semiannual period

Ask yield for May 39 bond is 4.151%.

For half year (i)= 4.151%/2= 0.020755

Coupon rate = 6.193%

Semiannual coupon rate = 6.193%/2= 0.030965

Coupon Amount = 1000*0.030965 = 30.965

Years to maturity= may 2019 to May 2039 = 20

Semiannual periods (n) =20*2 = 40

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

30.965*(1-(1/(1+0.020755)^40))/0.020755 + 1000/(1+0.020755)^40

1275.636704

So, Ask price of bonds in Dollars is $1275.64

B.

Ask price in % = Ask price/face value*100

In % quoted price = 1275.636704/1000

1.275636704

Bid ask Spread = 0.0566

So Bid price in % = Asked price + Bid ask spread

1.275636704+0.0566

1.332236704 or

133.224%

Bid price in Dollars = Bid price in %* Par value

133.224%*1000

1332.24 So Bid price in Dollars is $1332.24