Question

You find the following Treasury bond quotes. To calculate the number of years until maturity, assume...

You find the following Treasury bond quotes. To calculate the number of years until maturity, assume that it is currently May 2016. The bonds have a par value of \$1,000.

 Rate Maturity Mo/Yr Bid Asked Chg Ask Yld ?? May 22 103.5410 103.6288 +.3248 2.249 6.052 May 27 104.4900 104.6357 +.4245 ?? 6.143 May 37 ?? ?? +.5353 3.951

In the above table, find the Treasury bond that matures in May 2022. What is the coupon rate for this bond? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Coupon rate             %

Treasury bond that matures in May 2022 is the first bond.

Here we need to find the coupon rate of the bond. The price of the bond is:

Dollar price = 103.6288% × \$1,000

Dollar price = \$1,036.288

So the bond price equation is:

P = \$1,036.288 = C (PVIFA 1.1245%,12 ) + \$1,000(PVIF 1.1245%,12 )

Solving for the coupon payment, we get:

1036.288 = C(11.17) + 874.43

C = 161.861/11.17

C = \$14.49

Since this is the semiannual payment, the annual coupon payment is:

2 × \$14.49 = \$28.99

And the coupon rate is the coupon rate divided by par value, so:

Coupon rate = \$28.99 / \$1,000

Coupon rate = .02899or 2.90%