Question

The market price of a semi-annual pay bond is $977.53. It has 17.00 years to maturity and a coupon rate of 8.00%. Par value is $1,000. What is the effective annual yield?

(If someone can actually write out the steps not just show excel charts please)

Answer 1

)^)Face value= 1000

time (n) semiannual periods =17*2= 34

price = 977.5300

Semiannual Coupon = 1000*8%/2= 40

We will Calculate r by trial and error method. r is that rate where bond price is equal to Current bond price.

Bond price formula = Coupon amount * (1 - (1/(1+r)^n)/r + face value/(1+r)^n

Assume r= 4.50%

Bond price = 40*(1-(1/(1+4.5%)^34))/4.5%+ 1000/(1+4.5%)^34

913.7662102

Assume r= 4.00%

Bond price = 40*(1-(1/(1+4%)^34))/4%+ 1000/(1+4%)^34

1000

interpolation formula = lower rate + (uper rate - lower rate)*(Uper price - bond actual price)/(uper price - lower price)

4% + ((4.5%-4%)*(1000-977.53)/(1000-913.7662102))

0.04130285356

Semiannual yield to Maturity (I)= 0.04130285356

effective annual yield =((1+yield semiannual Rate)^no of Semiannual periods in year)-1  

=((1+0.04130285356)^2)-1

=0.08431163283 or 8.43%

Note: due to calcultion manually, there may be 0.01%+- in answer