A bond promises to pay $100 in one year. a. What is the interest rate on...
A bond promises to pay $100 in one year.
a. What is the interest rate on the bond if its price today is
$75? $85? $95?
b. What is the relation between the price of the bond and
the interest rate?
c. If the interest rate is 8%, what is the price of the bond today?
Homework Answers
(a) A bond promise to pay $100 in one year.
hence the face value of the bond is $100.
If its price of bond today is $75
Interest rate on the bond = ($100 / $75) - 1
Interest rate on the bond = 33.33%.
If its price of bond today is $85
Interest rate on the bond = ($100 / $85) - 1
Interest rate on the bond = 17.65%
If its price of bond today is $95
Interest rate on the bond = ($100 / $95) - 1
Interest rate on the bond = 5.26%
(b) There is negative relationship between price of the bond and the interest rate.
As we have seen that in part (a), increase in price of bond from $75 to %95 leads to decrease in interest rate from 33.33% to 5.26%.
(c) If the interest rate is 8%.
The price of bond = Face value of bond / (1 + Interest rate)
The price of bond = $100 / ( 1+ 0.08)
The price of bond = $100 / 1.08
The price of bond = $92.59
The price of bond = $92.60
Note: The price of bond = Face value of bond / (1 + Interest rate)
The price of bond (1 + Interest rate ) = Face value of bond
(1 + Interest rate ) = Face Value of bond / The price of bond
Interest rate = (Face value of bond / The price of bond) - 1
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