I bought a 4-week T-Bill at par amount $4,000 at price per $100 being $99.65. My issue date was 1/31/2023 and maturity date being 02/28/2023.

My Investment/Interest rate was 4.579% and my yield was 4.50%.

My discount (interest earned) is $14.00.

Not sure if my calculations are proper. Let me establish some notation:

R = return
Par Amount/Face Value = PA
Purchase Price = PP
Annual Return = APY

R = [(PA/PP)] / PP = [(4,000/3,986)] / 3,986 = 0.35%

APY = ((1 + r/n)^{n/m}-1) * 100

Where:

R = 0.0035 (defined above)
n = 52/4 = 13 (number times compounded per year) [I'm assuming this, not sure]
m = number months = 12

APY = ((1 + 0.0035/13)^{13/12} - 1) * 100 = 4.30%.

Are the 4.579% and 4.50% advertised (at auction) interest subject to volatility or something, or is my math wrong?

Wish I could format this with LaTex for you all, it'd be easier to read. I'm pretty sure r/personalfinance doesn't support the plugin.

Thanks!

Comments

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1hotjava t1_jadj8ok wrote on February 28, 2023 at 5:40 PM

#2,114,353

There is no compounding on a T-bill.

You have to get more refined. Use days, not months. Include cents and fractions of a cent. You didn’t buy at $99.65, it’s like $99.65113 (or whatever, I didn’t look yours up for the exact)

See top of page 2 here:

https://www.treasurydirect.gov/instit/annceresult/press/preanre/2004/ofcalc6decbill.pdf

CrimsonRaider2357 t1_jadjps3 wrote on February 28, 2023 at 5:43 PM

#2,114,507

Are you trying to calculate the annualized yield, or an APY?

Annualized yield: (4000/3986)^(365/28) -1 = 4.68%

APY: (4000/3986 - 1)(365/28) - 1 = 4.58%

hamta_ball OP t1_jadjqw6 wrote on February 28, 2023 at 5:44 PM

#2,114,518

Replying to 1hotjava (#2,114,353)

Thanks for this document!

PetMeFeedMeCuddleMe t1_jaeg9va wrote on February 28, 2023 at 9:10 PM

#2,125,428

Replying to 1hotjava (#2,114,353)

I looked up his bill. The auction cleared at $99.650000.

PetMeFeedMeCuddleMe t1_jaeha30 wrote on February 28, 2023 at 9:16 PM

#2,125,812

T bills are sold at a discount. You do not get any coupon payments. The equivalent issue yield is a calculation that is done to allow you to benchmark the bills' yield against yielding securities such as notes and bonds.

I wouldn't worry too much about the calculation, it is not the same formula as an APY calculation, but I have done it below for you. The point of the matter is for you to use ECY as a benchmark.

So, your bill, 912796Y78, cleared at a price of 99.65. The formula is (Face -price)/price * (365/maturity in days) because treasuries use an actual/365 day count convention.

Face = 100, price = 99.65. plug the numbers in and you get the ECY.

brundylop t1_jaeuvs1 wrote on February 28, 2023 at 10:47 PM

#2,131,366

Your 99.65 investment went up to 100.00 in 28 days.

That is a 0.351% increase in 28 days. To annualize it, multiply by 365.25 and divide by 28

Which comes out to 4.58%