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Answer: 7.14737% per annum with continuous compounding
A Treasury bill quoted at 7.00 is interpreted as a **discount rate** of 7.00% on a 360-day basis. 1. Compute the bill price: \[ P = 100\left(1 - 0.07\times\frac{72}{360}\right)=98.6 \] 2. Convert this to a continuously compounded return over 72 days, annualized on an actual/365 basis: \[ r = \frac{365}{72}\ln\left(\frac{100}{98.6}\right) \approx 0.07147 \] So the continuously compounded return is approximately **7.14737% per annum**.
Author: Manit Arora
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Question 719.2. The price of a 72-day Treasury bill is quoted as 7.00. Which is nearest to the continuously compounded return (on an actual/365 basis) that an investor will earn on the Treasury bill for the 72-day period? (note: inspired by Hull's EOC Problem 6.8)
A
1.40000% per annum with continuous compounding
B
5.60000% per annum with continuous compounding
C
5.71790% per annum with continuous compounding
D
7.14737% per annum with continuous compounding
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