What are the discount yield and the true annual yield on a s

What are the discount yield and the true annual yield on a six-month, $10,000 Treasury bill purchased for $9,589?

Solution

Discount yield is a measure of a bond\'s percentage return. Discount yield is most frequently used to calculate the yield on short-term bonds and treasury bills sold at a discount. This yield calculation uses a 30-day month and 360-day year to simplify calculations. Discount yield is calculated by the following formula:

Discount Yield = [(par value - purchase price)/par value] X [360/days to maturity]

So,

= [($10,000-$9589)/$10,000] X [360/(30*6)]

= [0.0411] X [2]

= 0.0822

True Annual Yield: Treasury bill is the classic example of a pure discount instrument, where the interest the government pays is the difference between the amount it promises to pay back at maturity (the face value) and the amount it borrowed when issuing the T-bill (the discount). A True/ Effective Annual Yield (EAY) can be computed as follows:

EAY = (1 + HPY)^365/t - 1

Holding-Period Yield (HPY) = (P₁ - P₀ + D₁)/P₀
Where: P₀ = purchase price, P₁ = price at maturity, and D₁= cash distribution at maturity

= ($10,000-$9589+0)/$10,000

= 0.0411

So,

EAY = (1+ 0.0411)^365/180 – 1

= 0.0839