Question

The BEY of a 182 day,$100000 T-Bill, Sold at a 4.53% discount rate. The BEY?

a. 4.01

b.4.64

c.4.70

d.5.20

Answer 1

Solution :

Calculation of the T-bill’s discount yield:                                

The formula for calculation of discount yield of a T-Bill when the No. of days in a year = 360

= [ (Face value – Purchase Price)/ Face value ] * ( 360 / No. of days to maturity )

As per the Information given in the question we have

Face Value = $ 100,000   ;

No. of days to maturity = 60

Discount yield = 4.53 % = 0.0453

Purchase Price = To find

Applying the above values in the formula we have

0.0453 = [ ( 100,000 – Purchase Price ) / 100,000 ] * ( 360 /182 )

( 0.0453 * 182 ) / 360 = [ ( 100,000 – Purchase Price ) / 100,000 ]

0.0229017 * 100,000 = ( 100,000 – Purchase Price )

2,290.1667 = ( 100,000 – Purchase Price )

Purchase price = 100,000 – 2,290.1667

Purchase price = 97,709.8333

Calculation of the T-bill’s Bond Equivalent yield:                

The formula for calculation of Bond equivalent yield of a T-Bill when the No. of days in a year = 365

= [ (Face value – Purchase Price)/ Purchase Price ] * ( 365 / No. of days to Maturity)

As per the Information given in the question we have

Face Value = $ 100,000   ;

Purchase Price = $ 97,709.8333

No. of days to maturity = 182

Applying the above values in the formula we have

= [ ( 100,000 – 97,709.8333 ) / 97,709.8333] * ( 365 / 182 )

=( 2,290.1667 / 97,709.8333 ) * 2.0054

= 0.02344 * 2.00549

= 0.0470 = 4.70 %

Thus the BEY of a 182 day, $100,000 T-Bill, Sold at a 4.53% discount rate = 4.70 %

Thus the Solution is Option c.4.70