# How do I determine Interest Rate of 4-Week Treasury Bill

I purchased 4 week treasury bill for \$2220

Treasury will take out \$2212.4545 from my Bank account

Treasury says Investment rate = 4.446% and High rate = 4.370%

But I calculate interest rate as 4.43361% (end of message)

How do I determine the Interest rate? Am I correct? Please advise.

``````2220 - 2212.4545 = 7.54550

100 * (7.54550 / 2212.4545) = 0.34105%

0.34105% * (52 weeks / 4 weeks ) =

0.34105% * (13) = 4.43361%
``````
• Are you sure about buying \$2200 in tbills, the treasury requires purchases in \$100 increments. Commented Jan 15, 2023 at 20:17
• Should you be allowing for interest compounding? Commented Jan 15, 2023 at 21:11
• @mhoran_psprep it is an example. please guide. Commented Jan 23, 2023 at 19:15
• @keshlam I don’t believe there is interest compounding. If there is interest compounding, please guide. Commented Jan 30, 2023 at 17:27
• @mhoran_psprep isn’t \$2200 an even multiple of \$100? Commented Nov 22, 2023 at 3:48

## 1 Answer

A good resource appears to be this link: https://www.treasurydirect.gov/instit/annceresult/press/preanre/2004/ofcalc6decbill.pdf which contains formulas that I will use in the answer.

Because of terminology used in the above document, specifically "Coupon Equivalent Yield," this needs to be combined with the statement from https://home.treasury.gov/resource-center/data-chart-center/interest-rates/TextView?type=daily_treasury_bill_rates&field_tdr_date_value_month=202208 , which is:

The Bank Discount rate is the rate at which a bill is quoted in the secondary market and is based on the par value, amount of the discount and a 360-day year. The Coupon Equivalent, also called the Bond Equivalent, or the Investment Yield, is the bill's yield based on the purchase price, discount, and a 365- or 366-day year. The Coupon Equivalent can be used to compare the yield on a discount bill to the yield on a nominal coupon security that pays semiannual interest with the same maturity date.

... which tells us that "Coupon Equivalent Yield" is the same as the "Investment Yield".

For your case, given the period of 4 weeks, the par value of \$2220 and the price of \$2212.4545, it is possible to calculate the discount rate and the investment rate as follows:

From the "Convert Price to Discount Rate" equation:

``````discount_rate = 360 days / period * ( 1 - price / par value)
discount_rate = 360 / 28 * (1 - 2212.4545 / 2220)
discount_rate = 0.043699807 ~= 0.0437
``````

From the "Calculate Coupon Equivalent Yield (For bills of not more than one half-year to maturity)" equation:

``````investment_rate = (par value / price - 1) * 365 days / period
investment_rate = (2220 / 2212.4545 - 1) * 365 / 28
investment_rate = 0.04445786 ~= 0.04446
``````

Note that you'll use 366 instead of 365 for the investment rate (coupon equivalent yield) equation, if February 29th occurs over the course of the year following the date of issue of the T-Bill. For instance, the investment yields for November 2023 use 366 days, because February 29th is within the next 365 days, whereas the investment yield for your example, where the coupon is issued in January, 2023, uses 365 days.