What is the price of Australian treasury note with exactly 70 days to maturity, a face value of $100,000 andan annualized yield to maturity of 1.64%.A. $98,386.46B. $99,686.47C. $99,688.52D. $99,836.00
Question
What is the price of Australian treasury note with exactly 70 days to maturity, a face value of 98,386.46B. 99,688.52D. $99,836.00
Solution
To calculate the price of a treasury note, we can use the formula for the price of a zero-coupon bond, which is:
P = F / (1 + r/n)^(nt)
Where: P = price of the bond F = face value of the bond r = annual yield to maturity n = number of times interest is compounded per year t = time to maturity in years
In this case, the face value F is $100,000, the annual yield to maturity r is 1.64% or 0.0164 (in decimal form), and the time to maturity t is 70 days. Since the yield is annualized, we'll assume that interest is compounded once per year (n = 1), and we'll convert the time to maturity to years by dividing by 365.
So, we have:
P = $100,000 / (1 + 0.0164/1)^(1*(70/365))
Now, we can calculate the price:
P = $100,000 / (1 + 0.0164)^(0.1917808219)
P = $100,000 / 1.0164^(0.1917808219)
P = $100,000 / 1.0031
P = $99,688.52
So, the price of the Australian treasury note with exactly 70 days to maturity, a face value of 99,688.52. Therefore, the correct answer is C. $99,688.52.
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