Yan Yan Corp. has a $5,000 par value bond outstanding with a coupon rate of 4.6 percent paid semiannually and 21 years to maturity. The yield to maturity on this bond is 4.1 percent. What is the price of the bond?

Price of the bond = $4,122.36

Explanation:

The value of the bond is the present value(PV) of the future cash receipts expected from the bond. The value is equal to present values of interest payment plus the redemption value (RV).  

Value of Bond = PV of interest + PV of RV  

The value of bond for Yan Yan Corp.  be worked out as follows:  

Step 1  

PV of interest payments  

Semi annul interest payment  

= 4.6% × 5,000 × 1/2 = 115

Semi-annual yield = 4.1%/2 = 2.05  % per six months  

Total period to maturity (in months)   = (2 × 21) = 41 periods

PV of interest =  

115  × (1- (1+0.0205)^(-21)/0.0205)=1,946.47

Step 2  

PV of Redemption Value  

= 5000 × (1.0205^(-41)   = 2,175.89

Step 3:Price of the bond

Total present Value = 1,946.47  +  2,175.89  = 4,122.36

Price of the bond = $4,122.36

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