Question

A coupon bond that pays interest of $40 semi-annually has a par value of $1,000, matures in four years, and is selling today at a $36 discount from par value. The yield to maturity on this bond is

I need the answer to be worked out by hand and step-by step. I need to know where all the numbers come from

Answer 1

Par Value = $1,000
Semiannual Coupon = $40

Time to Maturity = 4 years
Semiannual Period = 8

Discount = $36

Current Price = Par Value - Discount
Current Price = $1,000 - $36
Current Price = $964

Let Semiannual YTM be i%

$964 = $40 * PVIFA(i%, 8) + $1,000 * PVIF(i%, 8)

Using financial calculator:
N = 8
PV = -964
PMT = 40
FV = 1000

I = 4.547%

Semiannual YTM = 4.547%
Annual YTM = 2 * 4.547%
Annual YTM = 9.094% or 9.09%

So, the yield to maturity on this bond is 9.09%