Question

A treasury bill with 64 days to maturity is quoted at 99.012. what is the bank discount yield, the bond equivalent yield, and the effective annual return?

PLEASE SHOW CALCULATION FOR EAR

i got 5.558% for the discount yield and 5.691% for the bond equivalent yield.

Answer 1

To calculate the bank discount yield, use the formula: Bank Discount Yield = (Discount / Face Value) x (360 / Days To Maturity). For the bond equivalent yield, use the formula: Bond Equivalent Yield = 2 x Bank Discount Yield x (365 / Days To Maturity). The effective annual return (EAR) can be calculated using the formula: EAR = (1 + Bond Equivalent Yield)^(365 / Days To Maturity) - 1.

Step-by-step explanation:

To calculate the bank discount yield, we can use the formula:
Bank Discount Yield = (Discount / Face Value) x (360 / Days To Maturity)
where Discount = Face Value - Purchase Price. So in this case: Discount = 1000 - (99.012 x 1000) = 1000 - 99012 = -98012. The negative sign indicates that the purchase price is less than the face value. Using the formula, we get:
Bank Discount Yield = (-98012 / 1000) x (360 / 64) = -98.012 x 5.625 = -551.51%.

To calculate the bond equivalent yield, we can use the formula:
Bond Equivalent Yield = 2 x Bank Discount Yield x (365 / Days To Maturity)
Using the bank discount yield we calculated earlier, we get:
Bond Equivalent Yield = 2 x (-551.51%) x (365 / 64) = -1103.02 x 5.703125 = -6295.17%.

To calculate the effective annual return (EAR), we can use the formula:
EAR = (1 + Bond Equivalent Yield)^(365 / Days To Maturity) - 1
Using the bond equivalent yield we calculated earlier, we get:
EAR = (1 + (-6295.17%))^(365 / 64) - 1 = (1 - 62.9517)^(5.703125) - 1 = -0.999999982 - 1 = -1.999999982.