How to Calculate Interest on 90 Day Treasury Bills

How to Calculate Interest on 90 Day Treasury Bills
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Treasury bills, also known as T-bills, are short-term debt instruments with maturity terms of four, eight, 13, 26 and 52 weeks. T-bills are usually issued at a discount to par or face value, and the investor gets the face value back on maturity. The difference between the face value and the purchase price is the interest, also known as the yield. T-bills are sold in increments of $100, which is also the minimum purchase.

Two Types of Calculations

You can calculate the interest on T-bills (the yield) by using either the discount yield method or the investment yield method. Both types of computations use the same three values – the face value, the purchase price and the maturity of the issue.

The discount yield method compares an investor's return on investment to the face value of a bill. The investment yield method compares an investor's return on investment to the purchase price of a bill. When you use the discount yield method, you run the risk of understating yields as compared to using the investment yield method.

Obtaining the Purchase Price

The U.S. Treasury auctions the four-, eight, 13- and 26-week T-bills every week, and publishes the average, high and low prices. The 52-week T-bills are auctioned every four weeks. They can be purchased directly from the U.S. Department of Treasury's TreasuryDirect website (TreasuryDirect.gov), banks and brokers. Investors can hold on to the bills until maturity or sell them before maturity.

Calculating by Discount Yield Method

Calculate the interest rate using the discount yield method. The formula is: [100 x (FV - PP) / FV] x [360 / M], where FV is the face value, PP is the purchase price, 360 is the number of days used by financial institutions to compute the discount yield of short-term investments and "M" is the maturity in days. Note that "M" is equal to 91 days for a 90-day T-bill because the official maturity term is 13 weeks [13 x 7 = 91].

For example, if the average price of a 90-day T-bill, with a par value of $1,000, is $991.50, the yield or interest rate using the discount yield method is 3.363 percent: [100 x ($1,000 - $991.50) / $1,000 x (360 / 91) = 100 x 0.0085 x 3.95604 = 3.363].

Calculating by Investment Yield Method

Calculate the interest rate using the investment yield method. The formula is: [100 x (FV - PP) / PP] x [365 / M]. Note two differences with the discount yield method: First, the yield is calculated as a percentage of the purchase price rather than the par value; and second, the number of calendar days is used: 365 for regular years, 366 for leap years.

For the same T-bill example, the interest rate using the investment yield method is 3.439 percent: [100 x ($1,000 - $991.50) / $991.50 x (365 / 91) = 100 x 0.008573 x 4.010989 = 3.439]. This method results in a slightly higher yield than the discount yield method.

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