3. Suppose you have purchased a bond with a coupon rate of 8% that makes interes

Question

3. Suppose you have purchased a bond with a coupon rate of 8% that makes interest payments semi-annually, a yield to maturity (hint: this is the annual figure) of 6.5%, and a par value of $1000.

            a. If the bond matures in 5 years, what is the price of the bond?

b. Suppose that you wish to purchase the bond above on April 15, and its quoted price is the value that you calculated in part a. The bond makes coupon payments on January 1st and July 1st of each year, what is the invoice price of the bond? For simplicity, assume there are 30 days in each month of the year.  

Explanation / Answer

a) If the bond matures in 5 years, what is the price of the bond?

Given : The bond has a coupon rate of 8% that makes interest payments semi-annually, a yield to maturity (hint: this is the annual figure) of 6.5%, and a par value of $1000.

The Formula for Bond price on maturity is as follows :

Bond Price = 8/0.065 [ 1 - 1/(1.02) ^10]+ 1000/(1.02)^10

= $ 842.46

b) Bond Price on April 15th

Price as above = $ 842.46 + Interest Coupon Rate @ 8% for the period January to April 15th = 3-1/2 months on Face value of $ 1,000 = $ 23.33

Therefore, price = $ 865.79

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