Treasury T-Bill Rates ?

#3 07-25-2006, 02:12 PM

"Mark Freeland" <netnews[at]pacbell.net> wrote in message
news:1153821677.452681.232940[at]h48g2000cwc.googlegroups.com...
- quote -

> nearly_blind[at]yahoo.com wrote:
> > ...
> > E.g.
> > Term Issue - 91-DAY
> > Discount Rate %- 4.975 %
> > Investment Rate %- 5.108
> > Price per $100: 98.742431
> > > [...]
> > Of course I can just use the discount price (e.g.
98.742431) to
> > compute my own interest rate (based on whatever
compounding
> > I choose, e.g. continuous, daily, monthly ) or the
annual yield, but no
> > matter what
> > parameters and compounding method I use to calculate an
interest rate
> > based on the
> > return (100/98.742431) the result never agrees EXACTLY
with the
> > either the "discount" or "investment" rate shown.
> > > What are the exact formulas used to derive these two
rates based
> > on the TERM=91 days, and the return (100/98.742431).
> No compounding; just simple interest. You use a 360 day
calendar for
> discount rate, and a 365 (or 366) day calendar for
investment rate.
> See:
> http://www.ny.frb.org/aboutthefed/fedpoint/fed28.html
> [100 - 98.742431]/100 * 360/91 = 4.975% discount rate
> [100 - 98.742431]/98.742431 * 365/91 = 5.108% investment
rate
> Mark Freeland

Thank you Mark! I previously asked this question of
Treasury Direct several times, and only got gibberish as
answers. I have told them that your info should be included
on their site.

======================================= MODERATOR'S COMMENT:
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#2 07-25-2006, 12:20 PM

nearly_blind[at]yahoo.com wrote:
- quote -

> ...
> E.g.
> Term Issue - 91-DAY
> Discount Rate %- 4.975 %
> Investment Rate %- 5.108
> Price per $100: 98.742431
> [...]
> Of course I can just use the discount price (e.g. 98.742431) to
> compute my own interest rate (based on whatever compounding
> I choose, e.g. continuous, daily, monthly ) or the annual yield, but no
> matter what
> parameters and compounding method I use to calculate an interest rate
> based on the
> return (100/98.742431) the result never agrees EXACTLY with the
> either the "discount" or "investment" rate shown.
> What are the exact formulas used to derive these two rates based
> on the TERM=91 days, and the return (100/98.742431).

No compounding; just simple interest. You use a 360 day calendar for
discount rate, and a 365 (or 366) day calendar for investment rate.
See:

http://www.ny.frb.org/aboutthefed/fedpoint/fed28.html

[100 - 98.742431]/100 * 360/91 = 4.975% discount rate
[100 - 98.742431]/98.742431 * 365/91 = 5.108% investment rate

Mark Freeland

#1 07-25-2006, 12:20 PM

I think ,you pay, the interest rate subtracted from the $1000, and they pay
you back the $1000 at the end of the period.
<nearly_blind[at]yahoo.com> wrote in message
news:1153798763.617980.67020[at]m73g2000cwd.googlegroups.com...
- quote -

> I am very familar with all methods of interest computation
> and definitions of interest, annual yields, etc. , but cannot
> figure out (reverse engineer) how they derive either the
> "discount rate" or "investment rate" shown on the
> "Recent Treasury Auction Results" US Treasury page:
> http://wwws.publicdebt.treas.gov/AI/OFBills
> E.g.
> Term Issue - 91-DAY
> Discount Rate %- 4.975 %
> Investment Rate %- 5.108
> Price per $100: 98.742431
> (The T-bill is basically a zero coupon bond where in
> this example you pay $98.742431 now and get $100.00 back in 91 days).
> Of course I can just use the discount price (e.g. 98.742431) to
> compute my own interest rate (based on whatever compounding
> I choose, e.g. continuous, daily, monthly ) or the annual yield, but no
> matter what
> parameters and compounding method I use to calculate an interest rate
> based on the
> return (100/98.742431) the result never agrees EXACTLY with the
> either the "discount" or "investment" rate shown.
> What are the exact formulas used to derive these two rates based
> on the TERM=91 days, and the return (100/98.742431).
> Thanks.

07-25-2006, 12:01 PM

(100-98.742431)*(360/91)=4.97499 ~ 4.975

((100/98.742431)-1)*(365/91) = .05108336 ~ .5108

I too struggled with that sometime back.

joetaxpayer.com

nearly_blind[at]yahoo.com wrote:

- quote -

> I am very familar with all methods of interest computation
> and definitions of interest, annual yields, etc. , but cannot
> figure out (reverse engineer) how they derive either the
> "discount rate" or "investment rate" shown on the
> "Recent Treasury Auction Results" US Treasury page:
> http://wwws.publicdebt.treas.gov/AI/OFBills
> E.g.
> Term Issue - 91-DAY
> Discount Rate %- 4.975 %
> Investment Rate %- 5.108
> Price per $100: 98.742431
> (The T-bill is basically a zero coupon bond where in
> this example you pay $98.742431 now and get $100.00 back in 91 days).
> Of course I can just use the discount price (e.g. 98.742431) to
> compute my own interest rate (based on whatever compounding
> I choose, e.g. continuous, daily, monthly ) or the annual yield, but no
> matter what
> parameters and compounding method I use to calculate an interest rate
> based on the
> return (100/98.742431) the result never agrees EXACTLY with the
> either the "discount" or "investment" rate shown.
> What are the exact formulas used to derive these two rates based
> on the TERM=91 days, and the return (100/98.742431).
> Thanks.

#-1 07-25-2006, 09:07 AM

I am very familar with all methods of interest computation
and definitions of interest, annual yields, etc. , but cannot
figure out (reverse engineer) how they derive either the
"discount rate" or "investment rate" shown on the
"Recent Treasury Auction Results" US Treasury page:
http://wwws.publicdebt.treas.gov/AI/OFBills

E.g.
Term Issue - 91-DAY
Discount Rate %- 4.975 %
Investment Rate %- 5.108
Price per $100: 98.742431

(The T-bill is basically a zero coupon bond where in
this example you pay $98.742431 now and get $100.00 back in 91 days).

Of course I can just use the discount price (e.g. 98.742431) to
compute my own interest rate (based on whatever compounding
I choose, e.g. continuous, daily, monthly ) or the annual yield, but no
matter what
parameters and compounding method I use to calculate an interest rate
based on the
return (100/98.742431) the result never agrees EXACTLY with the
either the "discount" or "investment" rate shown.

What are the exact formulas used to derive these two rates based
on the TERM=91 days, and the return (100/98.742431).

Thanks.

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