bought T-Bill at Schwab for first time

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Nyc10036
Posts: 1310
Joined: Wed Oct 05, 2016 6:29 pm

bought T-Bill at Schwab for first time

Post by Nyc10036 »

I transfered $1000 into my Schwab account to buy 4-week T-Bill.
Today I received a trade notification email from Schwab which stated,

Code: Select all

Settle Date:	09/27/2022
Action:	Bought
Quantity:	1,000
Symbol:	US TREASURY BILL22U S T BILL DUE 10/25/22
Unit Price:	$99.7931
*Principal Amount:	$997.93
Does this mean that the interest rate is 2.07% ?

.
MedSaver
Posts: 237
Joined: Sun Jul 02, 2017 5:33 pm

Re: bought T-Bill at Schwab for first time

Post by MedSaver »

I'm not great with math, but wouldn't that be 0.207%?
increment
Posts: 1095
Joined: Tue May 15, 2018 2:20 pm

Re: bought T-Bill at Schwab for first time

Post by increment »

$2.07 is 0.207% of $1000 (and also 0.207% of $997.93, within rounding). But you get that in 4 weeks, roughly 1/13 of a year.
lstone19
Posts: 1648
Joined: Fri Nov 03, 2017 3:33 pm

Re: bought T-Bill at Schwab for first time

Post by lstone19 »

Nyc10036 wrote: Thu Sep 22, 2022 1:52 pm I transfered $1000 into my Schwab account to buy 4-week T-Bill.
Today I received a trade notification email from Schwab which stated,

Code: Select all

Settle Date:	09/27/2022
Action:	Bought
Quantity:	1,000
Symbol:	US TREASURY BILL22U S T BILL DUE 10/25/22
Unit Price:	$99.7931
*Principal Amount:	$997.93
Does this mean that the interest rate is 2.07% ?

.
No, it means you're paying $997.93 for a T-bill that will pay $1,000.00 at maturity for $2.07 in interest.

The interest rate can be calculated or it can be found in the auction results announcement:
Term: 4-Week
High Rate: 2.660%
Investment Rate*: 2.703%
Price: $99.793111
Allotted at High: 80.09%
Total Tendered: $143,654,916,700
Total Accepted: $52,706,246,700
Issue Date: 09/27/2022
Maturity Date: 10/25/2022
CUSIP: 912796YF0

*Equivalent coupon-issue yield

As stated above, the yield is 2.703% (the $2.07 interest on $997.93 annualized). The 2.660% "High Rate" is the annualized discount. Keep in mind that T-Bills are always sold at a discount so the yield is the interest on the discounted purchase price, not on the par value.

You can find the various Treasury announcements at https://www.treasurydirect.gov/instit/a ... /press.htm
student
Posts: 7369
Joined: Fri Apr 03, 2015 6:58 am

Re: bought T-Bill at Schwab for first time

Post by student »

No. $1000-$997.93=$2.07. This is the interest for 4 weeks, which is 28 days. So with simple interest with no compounding, you get $(2.07/28)*365, which is about $26.98. So the annual rate is about 2.704%. (Solving r in 997.93*r/100=26.98.)

Edit: Correcting an earlier mistake. Pricipal is $997.93, not $1000.
Last edited by student on Thu Sep 22, 2022 2:23 pm, edited 2 times in total.
Phil1234
Posts: 17
Joined: Wed Oct 28, 2015 8:55 pm

Re: bought T-Bill at Schwab for first time

Post by Phil1234 »

My understanding of the formula is:

Yield = 100*(100-price)/price

But then you can convert that to annualized return with the following formula:

Annualized return = Yield * 365/Days to maturity.

So in this case:

Yield = 100 * (100-99.7931)/99.7931 = 0.2073289636
Annualized return = 0.2073289636 * 365/28 = 2.702681133%. (This is a 4 week T-Bill or 28 days)

So annualized return is roughly 2.703%
Topic Author
Nyc10036
Posts: 1310
Joined: Wed Oct 05, 2016 6:29 pm

Re: bought T-Bill at Schwab for first time

Post by Nyc10036 »

lstone19 wrote: Thu Sep 22, 2022 2:09 pm
Nyc10036 wrote: Thu Sep 22, 2022 1:52 pm I transfered $1000 into my Schwab account to buy 4-week T-Bill.
Today I received a trade notification email from Schwab which stated,

Code: Select all

Settle Date:	09/27/2022
Action:	Bought
Quantity:	1,000
Symbol:	US TREASURY BILL22U S T BILL DUE 10/25/22
Unit Price:	$99.7931
*Principal Amount:	$997.93
Does this mean that the interest rate is 2.07% ?

.
No, it means you're paying $997.93 for a T-bill that will pay $1,000.00 at maturity for $2.07 in interest.

The interest rate can be calculated or it can be found in the auction results announcement:
Term: 4-Week
High Rate: 2.660%
Investment Rate*: 2.703%
Price: $99.793111
Allotted at High: 80.09%
Total Tendered: $143,654,916,700
Total Accepted: $52,706,246,700
Issue Date: 09/27/2022
Maturity Date: 10/25/2022
CUSIP: 912796YF0

*Equivalent coupon-issue yield

As stated above, the yield is 2.703% (the $2.07 interest on $997.93 annualized). The 2.660% "High Rate" is the annualized discount. Keep in mind that T-Bills are always sold at a discount so the yield is the interest on the discounted purchase price, not on the par value.

You can find the various Treasury announcements at https://www.treasurydirect.gov/instit/a ... /press.htm
Thank you.
I am horrible at these type of financial calculations.

student wrote: Thu Sep 22, 2022 2:13 pm No. $1000-$997.93=$2.07. This is the interest for 4 weeks, which is 28 days. So with simple interest with no compounding, you get $(2.07/28)*365, which is about $26.98. So the annual rate is about 2.704%. (Solving r in 997.93*r/100=26.98.)

Edit: Correcting an earlier mistake. Pricipal is $997.93, not $1000.
Thank you.
Last edited by Nyc10036 on Thu Sep 22, 2022 2:24 pm, edited 1 time in total.
ikowik
Posts: 256
Joined: Tue Dec 23, 2014 6:52 pm

Re: bought T-Bill at Schwab for first time

Post by ikowik »

student wrote: Thu Sep 22, 2022 2:13 pm No. $1000-$997.93=$2.07. This is the interest for 4 weeks, which is 28 days. So with simple interest with no compounding, you get $(2.07/28)*365, which is about $26.98. So the annual rate is about 2.698%. With compounding, it will be a bit less than 2.698%.
Rounding problem (cut off too many decimal points)
123
Posts: 8983
Joined: Fri Oct 12, 2012 3:55 pm

Re: bought T-Bill at Schwab for first time

Post by 123 »

student wrote: Thu Sep 22, 2022 2:13 pm No. $1000-$997.93=$2.07. This is the interest for 4 weeks, which is 28 days. So with simple interest with no compounding, you get $(2.07/28)*365, which is about $26.98. So the annual rate is about 2.698%. With compounding, it will be a bit less than 2.698%.
+1 I agree with student. They must have studied well.
The closest helping hand is at the end of your own arm.
student
Posts: 7369
Joined: Fri Apr 03, 2015 6:58 am

Re: bought T-Bill at Schwab for first time

Post by student »

ikowik wrote: Thu Sep 22, 2022 2:19 pm
student wrote: Thu Sep 22, 2022 2:13 pm No. $1000-$997.93=$2.07. This is the interest for 4 weeks, which is 28 days. So with simple interest with no compounding, you get $(2.07/28)*365, which is about $26.98. So the annual rate is about 2.698%. With compounding, it will be a bit less than 2.698%.
Rounding problem (cut off too many decimal points)
I made a mistake, not rounding problem. I used $1000 as principal but it should be $997.93. I have corrected the error with better explanation.
student
Posts: 7369
Joined: Fri Apr 03, 2015 6:58 am

Re: bought T-Bill at Schwab for first time

Post by student »

123 wrote: Thu Sep 22, 2022 2:20 pm
student wrote: Thu Sep 22, 2022 2:13 pm No. $1000-$997.93=$2.07. This is the interest for 4 weeks, which is 28 days. So with simple interest with no compounding, you get $(2.07/28)*365, which is about $26.98. So the annual rate is about 2.698%. With compounding, it will be a bit less than 2.698%.
+1 I agree with student. They must have studied well.
I actually made a mistake. I used $1000 as principal but it should be $997.93. I have corrected the error with better explanation.
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