A Treasury bill has 40 days left to maturity. The bank discount yield on the bill is 3.75%. What is the effective annual rate?

Question

Quizplus · Accepted Answer

First, we need to calculate the bank discount on the Treasury bill:
Bank Discount = Face Value * Bank Discount Yield * (Days to Maturity / 360)
Bank Discount = $1000 * 0.0375 * (40/360) = $3.75

The price of the Treasury bill can be calculated as follows:
Price = Face Value - Bank Discount
Price = $1000 - $3.75 = $996.25

Using the formula for the effective annual rate (EAR):
EAR = (1 + Bank Discount Yield * Days to Maturity / 360)^365/Days to Maturity - 1
EAR = (1 + 0.0375 * 40/360)^365/40 - 1
EAR = 0.0382 or 3.82%

Therefore, the answer is D) 3.82%.

A Treasury Bill Has 40 Days Left to Maturity