A Government of Canada T-bill with a face value of $1,000 and 45 days to maturity is trading for $985.22.The 45-day interest rate is ______ and the annual rate is ______.
A)1.5%, 12.17%
B)12.17%, 1.5%
C)1.5%, 12.84%
D)12.84%, 1.5%

Question

Quizplus · Accepted Answer

To calculate the 45-day interest rate:
Interest = Face Value - Trading Price
Interest = $1,000 - $985.22 = $14.78
Interest Rate = Interest / Face Value x (360 / days to maturity)
Interest Rate = $14.78 / $1,000 x (360 / 45)
Interest Rate = 0.01478 x 8 = 0.11824 or 11.82%
To convert the 45-day interest rate to an annual rate:
Annual Rate = (1 + 45-day interest rate)^(365/45)-1
Annual Rate = (1 + 0.11824)^(365/45)-1
Annual Rate = 1.1217 - 1
Annual Rate = 0.1217 or 12.17% 
Therefore, the correct answer is A.

A Government of Canada T-Bill with a Face Value of $1,000