Question

An investor buys a total of 360 shares-year bond with a $1,000 face value for $800. The bond's coupon rate is 8% and interest payments are made semi-annually. Waht are the bond's yield to maturity and effective annual yield?

Answer 1

Answer:

YTM (Annual( = 10.13%

Effective Annual Yield =10.40%  

Explanation:

In order to calculate Yield to maturity, we need to use yield to maturity formula.

Formula: Yield to maturity = [C +(F – P)/n]/(F + P)/2

Where,

C = Coupon amount

F = Face value

n = number of periods

P = Current price

Data

C =  1000 x 8 % = 80

C (6months) = 80 x 6/12 = 40

F = $1000

n = 30 years

P = $800

Solution

YTM = 40 + (1000 – 800/30)/(1000 + 800)/2

YTM = 40 + (200/30)/(1800/2 )

YTM = 40 +( 200/30)/900

YTM = 5.068 semiannual

YTM (Annual( = 10.13%

Effective Annual Yield = $(\frac{1+0.1014}{2})^{2-1}$

Effective Annual Yield =10.40%