Question

4.If a six-month Treasury bill is purchased for $0.9475 on a dollar (i.e., $94,750 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 $0.924 on a dollar (i.e., $92,400 for a $100,000 bill)?

Answer 1

a)
Discount yield = ($100,000 - $94,750) / $100,000 * 12/6 = 10.50%

Annual rate of return = ($100,000 - $94,750) / $94,750) * 12/6 = 11.08%

Compound rate can be calculated by using the following excel formula:
=RATE(nper,pmt,pv,fv)
=RATE(0.5,0,-94750,100000)
= 11.39%

Compound rate = 11.39%

b)
If discount price falls to $0.924:

Discount yield = ($100,000 - $92,400) / $100,000 * 12/6 = 15.20%

Annual rate of return = ($100,000 - $92,400) / $92,400 * 12/6 = 16.45%

Compound rate can be calculated by using the following excel formula:
=RATE(nper,pmt,pv,fv)
=RATE(0.5,0,-92400,100000)
= 17.13%

Compound rate = 17.13%