Question

A T-bill that is 290 days from maturity is selling for $96,040. The T-bill has a face value of $100,000.

a. Calculate the discount yield, bond equivalent yield, and EAR on the T-bill.
b. Calculate the discount yield, bond equivalent yield, and EAR on the T-bill if it matures in 365 days.

Answer 1

Answer: a 0.049, 0.05 and 0.05 or 5%

b 0.039, 0.041 and 0.041 or 4%

Step-by-step explanation:

Ai discounted yield = [(Face value - purchase price)/Face value] * 360/ maturity

Discount yield =:[(100000 - 96040)/100000] * 360/290

= 0.0396* 1.24

= 0.049

ii. Bond equivalent yield (BEY) = [(Face value - purchase price)/purchase value] * 365/M

BEY= [(100000 - 96040)/96040] * 365/290

BEY = 0.05

iii EAR = [(1+BEY/n)exp n - 1)

EAR = [(1 + 0.05/(365/290)) exp (360/290) - 1]

EAR = [(1 + 0.05/1.26) exp (1.26) - 1

EAR = (1.04) exp (1.26) - 1

EAR = 0.05 or 5%

The same formula are applied for the B part

Discount yield = [(100000-96040)/100000] * 360/365

Discount yield = 0.0396 * 0.986

= 0.039

B ii. BEY = [(100000 - 96040)/96040] * 365/365

BEY = 0.041 × 1

BEY = 0.041

B iii. EAR = [(1 + 0.041/(365/365))exp (365/365) - 1

EAR = (1 + 0.41) - 1

EAR = 0.041 or 4%