Final answer:
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.