Question

Your friend Earl is starting a dog-grooming service called "Petsgroom." Because his business is new and risky, he is unable to obtain a loan from the local bank. You agree to pay a price of $7,250 for a one-year bond from Earl.

a. Calculate the par value of the bond with an interest rate of 3.4%

b. Calculate the par value of the bond with an interest rate of 6.7%

c. Comment on the relationship between the purchase price of the bond and the interest rate

Answer 1

The par-value of the bond can be calculated by using the formula for bond price as given by -

BondPrice = (1+r)

This is thr formula for a zero coupon payment bond with a maturity period of one year, as the one stated in the question. Here F is the par valus of the bond. The Bonf Price given in the question is $7250.

a. When r=3.4% = 0.034

7250 = (1+0.034)

7250 = = 1.034)

→ (7250) * (1.034) = F

F = 7496.5

b. Similarly, whem r=6.7% = 0.067

7250= 1- 0.067)

一7250=1067) 7250、

(7250) * (1.067) = F

F = 7735.75

c. Bond prices usually fall when the interest rate rises and vice versa. This is because when the interest rate rises, the existing bonds which offer lower interest rate will not be favoured by people. Hence, the price of these old bonds will have to decrease enough to make their resultant yeild to maturity more favourable to the people than the new bonds that are offering a higher yeild to maturity. Hence, when interest rates rise, bond prices fall.