Suppose you purchase a T-bill maturing in 50 days which has a par value of $10,000 and a bank discount rate of 9

a. The T-bill’s discount rate = 9.50%

T- Bill’s discount rate = (D/F) * (360/t)

Where Face value F = $10,000

9.50% = (D/10000) * (360/50)

Or D = $131.944

Price P = F – D = $10,000 - $131.944

= $9,868.06

T-bill’s bond equivalent yield = (D/P) * (365/t)

= ($131.944/$9,868.06) * (365/50) = 0.09761 or 9.761%

b. Yield for 50 days on T-Bill = (F –P)/P = ($10,000 -$9,868.06)/ $9,868.06

= 0.01337 or 1.337%

Therefore, the annual percentage rate of return = 1.337% *(365/50) = 9.761% (which is equal to T-bill’s bond equivalent yield)

c. The T-bill’s bond EAR is calculated as below

EAR = [1 + T-bill’s bond equivalent yield / (365/t)] ^ (365/t) − 1

= [1 + 0.09761/ (365/50)] ^ (365/50) – 1

=0.10182 or 10.0182%