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	103.4638	103.5366	+.3041	6.039
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 2031. What is your yield to maturity if you buy this bond? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Yield to maturity             %

Answer 1

Face Value = $1,000

Current Price = 104.6435% * $1,000
Current Price = $1,046.435

Annual Coupon Rate = 6.173%
Semiannual Coupon Rate = 3.0865%
Semiannual Coupon = 3.0865% * $1,000
Semiannual Coupon = $30.865

Time to Maturity = 15 years
Semiannual Period = 30

Let Semiannual YTM be i%

$1,046.435 = $30.865 * PVIFA(i%, 30) + $1,000 * PVIF(i%, 30)

Using financial calculator:
N = 30
PV = -1046.435
PMT = 30.865
FV = 1000

I = 2.854%

Semiannual YTM = 2.854%
Annual YTM = 2 * 2.854%
Annual YTM = 5.708% or 5.71%

So, yield to maturity is 5.71%