8-Week Treasury Bill Rate Calculator
Calculated Yield
" + "Purchase Price: $" + purchasePrice.toFixed(2) + "" + "Bond Equivalent Yield: " + yield.toFixed(4) + "%"; }Understanding 8-Week Treasury Bills and Their Yield
Treasury Bills (T-Bills) are short-term debt instruments issued by the U.S. Department of the Treasury to finance government expenditures. They have maturities of one year or less, with common tenors including 4-week, 8-week, 13-week, 17-week, and 26-week bills. The 8-week Treasury Bill is a popular choice for investors seeking a safe, short-term investment with a predictable return.
How 8-Week Treasury Bills Work
Unlike traditional bonds that pay periodic interest (coupons), T-Bills are typically sold at a discount to their face value (par value). At maturity, the holder receives the full face value. The difference between the purchase price and the face value represents the investor's profit, which is essentially the interest earned.
The Discount Rate vs. Yield
When T-Bills are issued, they are often quoted using a "discount rate." This rate is used to determine the purchase price. However, the discount rate is not the actual rate of return an investor receives. To understand the true return, we calculate the Bond Equivalent Yield (BEY).
- Discount Rate: This is the annualized percentage discount from the face value, calculated on a 360-day year.
- Purchase Price: The price an investor pays for the T-Bill, which is less than the face value.
- Bond Equivalent Yield (BEY): This is the annualized yield an investor receives, calculated on a 365-day year and reflecting the actual return on the invested capital. It's the standard way to compare the returns of short-term T-Bills with other types of investments.
How the Calculator Works
Our 8-Week Treasury Bill Rate Calculator helps you determine the Bond Equivalent Yield based on three key inputs:
- Par Value: The face value of the Treasury Bill that will be repaid at maturity (e.g., $1,000).
- Discount Rate: The annualized discount rate at which the T-Bill is offered, typically quoted by the Treasury.
- Days to Maturity: The remaining time until the T-Bill matures. For an 8-week T-Bill, this is usually around 56 days.
The calculator first computes the actual Purchase Price of the T-Bill using the provided discount rate and days to maturity. It then uses this purchase price and the par value to calculate the Bond Equivalent Yield, giving you a clear picture of your investment's potential return.
Example Calculation
Let's say you are considering an 8-week Treasury Bill with:
- Par Value: $1,000
- Discount Rate: 5%
- Days to Maturity: 56 days
Using these figures, the calculator would first determine the purchase price. A 5% discount rate applied over 56 days on a $1,000 par value means the investor pays less than $1,000.
The formula for purchase price is:
Purchase Price = Par Value * (1 – (Discount Rate/100) * (Days to Maturity / 360))
Purchase Price = $1,000 * (1 – (5/100) * (56 / 360))
Purchase Price = $1,000 * (1 – 0.05 * 0.15555…)
Purchase Price = $1,000 * (1 – 0.00777…)
Purchase Price = $1,000 * 0.99222… ≈ $992.22
Next, the calculator determines the Bond Equivalent Yield:
Bond Equivalent Yield = ((Par Value – Purchase Price) / Purchase Price) * (365 / Days to Maturity) * 100
Bond Equivalent Yield = (($1,000 – $992.22) / $992.22) * (365 / 56) * 100
Bond Equivalent Yield = ($7.78 / $992.22) * 6.5178… * 100
Bond Equivalent Yield ≈ 0.00784… * 6.5178… * 100
Bond Equivalent Yield ≈ 5.1178%
So, for this example, the Bond Equivalent Yield is approximately 5.1178%. This means that, annualized, your investment of $992.22 would effectively earn about 5.1178% over the course of the year, even though the T-Bill only matures in 56 days.