A 11-year zero-coupon bond currently yields 2.56%. Suppose you compound 3 times per year, what is this bond's market price per $100 of face value? Report your answer with 2-digit precision (ex. 12.34).
Question
A 11-year zero-coupon bond currently yields 2.56%. Suppose you compound 3 times per year, what is this bond's market price per $100 of face value? Report your answer with 2-digit precision (ex. 12.34).
Solution
To calculate the price of a zero-coupon bond, we use the formula:
P = F / (1 + r/n)^(nt)
where: P = price of the bond F = face value of the bond r = yield or interest rate n = number of times interest is compounded per year t = time in years until maturity
Given in the problem: F = $100 (face value) r = 2.56% or 0.0256 (yield) n = 3 (compounded 3 times per year) t = 11 years
Substituting these values into the formula, we get:
P = 100 / (1 + 0.0256/3)^(3*11)
Now, calculate the value inside the parentheses:
1 + 0.0256/3 = 1.00853333333
Raise this to the power of 33 (3 times 11):
(1.00853333333)^(33) = 1.318364654
Now, divide the face value by this number:
P = 100 / 1.318364654 = 75.81
So, the bond's market price per 75.81.
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