Please help with this Thank you 1 At auction 6month Tbills w

Please help with this!!!! Thank you!!!!

1, At auction, 6-month T-bills were sold at a discount of 7.420%. What was the simple annual yield r? (Round your answer to three decimal places.)

r =....?

2, At auction, 2-month T-bills were sold at a discount of 5.510%. What was the simple annual yield r? (Round your answer to three decimal places.)

r =....?

Solution

It is not of my subjects, still I try.

1.)

T-bill discount means: if it\'s a 1-year maturity,
it is sold for (1 - discount ) percent.
If this were a 12-month T-bill, the price would be 93.580 per $100 purchased.

But this is only an 6-month T-bill, so everything is reduced by 1/2.
Instead of 7.420 %, the reduction is 3.710 % ( = 1/2 * 7.420)

You would buy $10,000 maturity value for 9629
and your return would be 10000/9629 = 1.0385
but that is for 6 months or 1/2 of a year,
as simple interest it would be 7.7 % (= 2/1 * 3.85)

2.)

T-bill discount means: if it\'s a 1-year maturity,
it is sold for (1 - discount ) percent.
If this were a 12-month T-bill, the price would be 94.490 per $100 purchased.

But this is only an 2-month T-bill, so everything is reduced by 5/6.
Instead of 5.510 %, the reduction is 0.9183 % ( = 1/6 * 5.510)

You would buy $10,000 maturity value for 9908.17
and your return would be 10000/9908.17 = 1.0093
but that is for 2 months or 5/6 of a year,
as simple interest it would be 1.116 % (= 6/5 * 0.93)