Question

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 26	103.5488	103.6370	+.3041	2.369
5.324	May 31	104.4978	104.6435	+.4317	??
6.173	May 41	??	??	+.5431	4.071

In the above table, find the Treasury bond that matures in May 2026. 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.)

Answer 1

Par Value = $1,000

Current Price = Asked Quote * Par Value
Current Price = 103.6370% * $1,000
Current Price = $1,036.37

Annual YTM = 2.369%
Semiannual YTM = 2.369% / 2
Semiannual YTM = 1.1845%

Time to Maturity = 10 years
Semiannual Period = 20

Let Semiannual Coupon be $C

$1,036.37 = $C * PVIFA(1.1845%, 20) + $1,000 * PVIF(1.1845%, 20)
$1,036.37 = $C * (1 - (1/1.011845)^20) / 0.011845 + $1,000 / 1.011845^20
$1,036.37 = $C * 17.714699 + $790.169388
$246.200612 = $C * 17.714699
$C = $13.90

Semiannual Coupon = $13.90

Annual Coupon = 2 *$13.90
Annual Coupon = $27.80

Coupon Rate = Annual Coupon / Par Value
Coupon Rate = $27.80 / $1,000
Coupon Rate = 0.0278 or 2.78%