the 6 semiannual coupon Bond IPO agency are selling for 1 08

the 6% semiannual coupon Bond IPO agency are selling for $1, 087 the bonds have a face value of 1000 and mature in 11 years what is the yield to maturity

Solution

Face Value = $1,000
Current Price = $1,087

Annual Coupon Rate = 6%
Semiannual Coupon Rate = 3%
Semiannual Coupon = 3% * $1,000
Semiannual Coupon = $30

Time to Maturity = 11 years
Semiannual Period to Maturity = 22

Let semiannual YTM be i%

$1,087 = $30 * PVIFA(i%, 22) + $1,000 * PVIF(i%, 22)

Using financial calculator:
N = 22
PV = -1087
PMT = 30
FV = 1000

I = 2.48%

Semiannual YTM = 2.48%
Annual YTM = 2 * 2.48%
Annual YTM = 4.96%