Question

4. (a) If a six-month Treasury bill is purchased for $0.9325 on a dollar (i.e., $93,250 for a $100,000 bill), what is the discount yield, the annual rate of interest, and the compound rate? What will these yields be if the discount price falls to $0.9045 on a dollar (i.e., $90,450 for a $100,000 bill)? (5 points)

PLEASE SHOW WORK

Answer 1

1.
Discount yield = ($100,000 - $93,250) / $100,000 * (12 / 6)
= $6750 / $100,000 * 2
= 13.5%

Annual rate of return = ($100,000 - $93,250) / $93,250 * (12 / 6)
= $6750 / $93250 * 2
= 14.48%

Compound rate can be calculated by using the following excel formula:
=RATE(nper,pmt,pv,fv)
=RATE(0.5,0,-93250,100000)
= 15.00%

Compond rate = 15.00%

If discount price falls to $0.9045:

Discount yield = ($100,000 - $90450) / $100,000 * (12 / 6)
= $9550 / $100,000 * 2
= 19.10%

Annual rate of return = ($100,000 - $90,450) / $90,450 * (12 / 6)
= $9550 / $90450 * 2
= 21.12%

Compound rate can be calculated by using the following excel formula:
=RATE(nper,pmt,pv,fv)
=RATE(0.5,0,-90450,100000)
= 22.23%

Compound rate = 22.23%