Question

Given the following information, find the yield to maturity (YTM)

DTD- 03/15/2014

Coupon rate- 4.625%

Maturity- 03/15/2024

market price- 93.749 per share (total market price= 22,812.50)

Cost price- 100.30 per share (total cost price = 25,813.25)

Answer 1

Face value (Assumed as per market price)   $100  
Transaction date=   03/15/2014  
maturity date=   03/15/2024  
So years to Maturity (n)   10   years
price = (market price)   93.7490  
Coupon = 100*4.625%=   4.625  
      
Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n      

Yield to maturity is that rate where bond price will be equal to current market price. So Assume i=6% or   0.06  
4.625*(1-(1/(1+0.06)^10))/0.06 + 100/(1+0.06)^10      
$89.88      

Assume i=5% or   0.05  
4.625*(1-(1/(1+0.05)^10))/0.05+ 100/(1+0.05)^10      
$97.10      

Now rate will be calculated by interpolation formula:
interpolation formula = lower rate + (uper rate - lower rate)*(Uper price - bond actual price)/(uper price - lower price      
=5% + (6%-5%)*(97.1-93.749)/(97-89.88)      
5.4544%      
So yield to maturity of bond is    5.45%  

(% can differ in points decimal places)