Question

there is a bond that has quoted a price of 107.324 and a par value of $2000. the coupon rate is 7.08 percent and the bonb matures in 18 years. if the bond makes semiannual coupon payments, what is the YTM of the bond?

Answer 1

Answer.
Face Value = $2,000
Current Price = $2,000 * 107.324%
Current Price = $2,146.48

Annual Coupon Rate = 7.08%
Semiannual Coupon Rate = 3.54%
Semiannual Coupon = 3.54% * $2,000 = $70.80

Time to Maturity = 18 years
Semiannual Period to Maturity = 36

Let semiannual YTM be i%

$2,146.48 = $70.80 * PVIFA(i%, 36) + $2,000 * PVIF(i%, 36)

Using financial calculator:
N = 36
PV = -2146.48
PMT = 70.80
FV = 2000

I = 3.1947%

Semiannual YTM = 3.1947%
Annual YTM = 2 * 3.1947%
Annual YTM = 6.39%