T Bill Return Calculator

Treasury bills are America's safest short term investment. The government sells them at a discount regularly. You pay less than the face value upfront. At maturity, you receive the full face value. The gap between those numbers is your profit. No coupons or interest payments arrive in between. That simple design still confuses many first time buyers. Two different yield figures describe the same bill. The calculator above untangles both of them quickly. You enter face value, price, and days held. It returns profit plus both annual yield measures.

This page explains why two yields exist at all. Worked examples then verify every figure by hand. Understanding both numbers helps you compare bills fairly. It also helps you compare bills against bank accounts.

Even experienced savers misread bill quotes surprisingly often. A quoted yield looks lower than a savings rate. Yet the bill may actually pay more after tax. The difference hides inside the quoting conventions themselves. Learning to convert between them protects your returns. Five minutes of study pays off for years.

What Is a Treasury Bill?

A Treasury bill is a short term government loan. Investors lend money to the United States Treasury. Terms run from four weeks to one year. Bills sell in increments of one hundred dollars. The Treasury auctions new bills every single week. Buyers bid a price below the face value. That discount replaces the usual interest payment entirely. At maturity, the Treasury pays full face value. Your return is locked in at purchase time. Defaults are considered virtually impossible by markets worldwide.

Bills suit cash you cannot afford to risk. Emergency funds often sit in bills for safety. Businesses park idle cash in bills too. Returns are modest but extremely predictable in advance. State and local taxes skip bill income entirely. Only federal income tax applies to the profit. That tax edge lifts bills above many alternatives.

Inflation is the one risk bills cannot dodge. Prices rising faster than yields shrink real returns. Short terms limit that exposure to brief windows. Buyers reprice their commitment every few months anyway.

Money market funds often hold bills behind the scenes. Buying directly simply removes the fund's small fee. Direct owners also control their maturity dates precisely. That control suits known future expenses very well.

Discount Yield Versus Investment Yield

The discount yield is the Treasury's traditional quote. It divides the profit by the face value. Then it annualises using a 360 day year. Both choices make the number look smaller. Face value exceeds your actual cash invested, remember. A 360 day year also understates real annual growth. Dealers still quote bills this way by convention. Knowing its bias helps you read quotes wisely. Never compare a discount yield against bank rates directly.

The investment yield corrects both of those biases. It divides profit by the price you paid. Then it annualises using a 365 day year. This figure is also called coupon equivalent yield. It matches how bonds and accounts express returns. Comparing investments becomes fair with this number. Our calculator shows both yields side by side. The gap between them surprises many new buyers.

A quick rule reveals which figure you are reading. Investment yield always exceeds the discount yield slightly. Identical inputs can never reverse that ordering relationship. Spotting a reversed quote means someone mislabelled it.

How the Return Is Calculated Step by Step

Start with the simple dollar return first. Subtract the purchase price from face value. That difference is your entire profit, in dollars. A ten thousand dollar bill bought for 9,750 returns 250. Next comes the holding period return percentage. Divide the profit by the price you paid. That shows growth over the actual days held. Annualising then stretches that growth to one year. Discount yield uses face value and 360 days. Investment yield uses price paid and 365 days.

Work through any bill in that fixed order. Dollar profit first keeps the scale grounded honestly. Percentages then describe that profit from two angles. Skipping straight to yields invites confusion between them. The order used here mirrors professional practice closely.

Price per one hundred is a dealer shorthand. It restates your price against each hundred of face. Paying 9,750 for 10,000 face equals 97.50 per hundred. Quotes in newspapers often use this compact format. Our calculator includes it for easy quote checking. All five outputs come from three simple inputs. No hidden fees or compounding tricks sit inside.

How to Use the T Bill Return Calculator

Three numbers from your auction confirmation are enough. Follow these steps for an accurate result.

1. Enter the face value paid at maturity.
2. Type the purchase price you actually paid.
3. Enter the days from purchase to maturity.
4. Press the blue Calculate button to run it.
5. Read the dollar return at the top.
6. Compare the discount and investment yields shown.
7. Check the price per hundred against your quote.

Worked Example 1: A 182 Day Bill for 9,750 Dollars

The Inputs

An investor buys a 10,000 dollar face value bill. She pays 9,750 dollars at auction today. The bill matures in 182 days exactly. Those three figures fill the calculator fields. Her profit and both yields follow from them.

She chose this term to match a tax payment. The money must stay safe until spring arrives. Growth matters, but certainty matters far more here.

The Calculation

First, the dollar return equals 10,000 minus 9,750. That subtraction gives a profit of 250 dollars. Holding period return divides 250 by 9,750 next. That equals 2.5641 percent over the 182 days. Discount yield divides 250 by the 10,000 face value. Then it multiplies by 360 over 182 days. The result is a 4.9451 percent discount yield. Investment yield divides 250 by the 9,750 price. Then it multiplies by 365 over 182 days. The result is a 5.1423 percent investment yield. Price per hundred equals 9,750 over 10,000 times one hundred. That gives exactly 97.50 per hundred of face. Notice the holding return covers only half a year. Annualising roughly doubles it, minus convention differences inside.

The Result

She earns 250 dollars over roughly six months. Her investment yield beats the discount yield clearly. The gap reaches almost twenty basis points here. Fair comparisons must use the 5.1423 percent figure. Bank offers can now be judged honestly against it.

Suppose a bank offered her 5.00 percent instead. The bill still wins before taxes enter the picture. State tax exemption then widens the bill's lead further. Examples like this explain the bill's loyal following.

Worked Example 2: A 91 Day Bill for 990 Dollars

The Inputs

A saver buys a small 1,000 dollar bill. He pays 990 dollars for it today. Maturity arrives in just 91 days time. Small bills follow the same rules as large ones. His results make a tidy second check.

The Calculation

First, the dollar return equals 1,000 minus 990. That subtraction gives a profit of 10 dollars. Holding period return divides 10 by 990 next. That equals 1.0101 percent over the 91 days. Discount yield divides 10 by the 1,000 face value. Then it multiplies by 360 over 91 days. The result is a 3.9560 percent discount yield. Investment yield divides 10 by the 990 price. Then it multiplies by 365 over 91 days. The result is a 4.0515 percent investment yield. Price per hundred equals 990 over 1,000 times one hundred. That gives exactly 99.00 per hundred of face. Quarterly bills like this suit short savings goals. College fees due next term are one example.

The Result

He earns 10 dollars over roughly three months. Shorter bills annualise small profits into respectable yields. His investment yield again tops the discount yield. Both examples confirm the same consistent pattern. Small inputs still deserve careful annual comparisons.

Rolling this bill four times compounds the effect slightly. Each quarter reinvests a slightly larger principal amount. Yearly growth therefore edges above the single yield. Ladders and rollovers reward patient small savers steadily.

Why the 360 Day Year Exists

The 360 day convention predates modern computing tools. Bankers once needed arithmetic that divided very cleanly. Twelve months of thirty days made hand calculation easy. Money markets kept the habit long after computers arrived. Discount yield therefore keeps the old convention alive. It is not a trick, just an old standard. Still, it understates the true yearly growth slightly. That is why the investment yield also exists. Quoting both keeps tradition and accuracy side by side.

Other money market tools share similar quirks globally. Commercial paper also uses discount style quoting often. Certificates of deposit instead quote simple annual rates. Comparing across products demands converting to one basis. The investment yield is the safest common basis. Use it whenever a bank product enters the comparison.

Leap years add one more tiny wrinkle sometimes. Some longer calculations switch to a 366 day count. Bills under six months keep the standard approach regardless. Our calculator follows the standard bill conventions throughout. Consistency matters more than the tiny difference involved.

Taxes and Safety Considerations

Bill profit counts as federal interest income yearly. You report it in the year the bill matures. Selling early also triggers reporting in that year. State and local income taxes never apply here. That exemption quietly boosts your after tax return. Residents of high tax states benefit the most. Safety is the other headline feature of bills. The full faith of the government backs them. No bank failure can touch a direct holding.

Bills held inside funds behave slightly differently though. Funds can fluctuate in price before maturity arrives. Direct holdings avoid that interim price noise completely. Selling a bill early also exposes you to prices. Hold to maturity and the return stays fixed. That certainty is the product's greatest selling point.

Laddering spreads maturity dates across several future months. Each rung matures and funds a planned expense. Remaining rungs keep earning until their own dates. This simple structure balances yield and ready access. Many savers automate reinvestment for the unused rungs.

Buying Bills Through Auctions and Brokers

The Treasury auctions bills on a regular weekly schedule. Four, eight, thirteen, seventeen, twenty six, and fifty two week terms exist. Noncompetitive bids accept whatever price the auction sets. Most individuals choose that simple route every time. Competitive bids suit institutions chasing tiny price edges. TreasuryDirect handles purchases without charging any commission fees. Brokers may add small fees but offer convenience. Secondary markets let you buy existing bills anytime.

Timing matters slightly when you buy through auctions. Orders must arrive before the auction deadline that day. Funds leave your linked bank account at issue. Maturity proceeds return to the same account automatically. Planning purchases around known expenses keeps cash productive. Idle cash between bill maturities earns nothing at all. Short gaps are normal and rarely worth worrying about. Longer gaps deserve a deliberate reinvestment plan instead.

Auction results publish on the same afternoon usually. High rate, average price, and investment rate appear. Compare your confirmation against those published figures carefully. Any mismatch deserves a quick call to your broker. Errors are rare, but checking costs you nothing.

Tips for Comparing Treasury Bill Returns

These habits keep your comparisons honest and useful. They apply to every maturity the Treasury offers.

1. Always compare using the investment yield figure.
2. Match maturities before comparing two bill quotes.
3. Remember state tax exemption in after tax comparisons.
4. Check the price per hundred against dealer quotes.
5. Hold to maturity when you need certainty.
6. Reinvest matured funds promptly to avoid idle cash.
7. Track auction dates, because terms start at purchase.

Frequently Asked Questions

General Questions

1. What is a Treasury bill?

It is a short term loan to the government. You buy it below its face value price. The Treasury repays full face value at maturity. Terms range from four weeks to one year.

2. Why do bills pay no interest payments?

The discount itself replaces regular interest payments entirely. You earn the gap between price and face. That gap arrives in full at maturity. Simple design keeps bills easy to trade.

3. How safe is money in Treasury bills?

Markets treat them as the safest dollar asset. The United States government guarantees repayment fully. Direct holdings face no bank failure risk. Only early sale prices can fluctuate.

4. What is the minimum purchase amount?

Bills sell in one hundred dollar increments. Most investors buy through TreasuryDirect or brokers. Small savers can start with a single increment. Larger buyers face very high maximum limits.

5. When do I receive my profit?

Profit arrives automatically at maturity with face value. The Treasury deposits the full amount directly. No separate interest payment ever appears beforehand. Reinvestment can be scheduled in advance too.

How the Calculation Works

6. How is the dollar return calculated?

Subtract the purchase price from face value. Ten thousand minus 9,750 gives 250 dollars. That difference is your entire investment profit. Nothing else adds to or trims it.

7. What is the discount yield formula?

Divide profit by the full face value. Then multiply by 360 over days held. Finally multiply by one hundred for percent. This is the Treasury's traditional quoting method.

8. What is the investment yield formula?

Divide profit by the price you paid. Then multiply by 365 over days held. Finally multiply by one hundred for percent. It matches bond and account quoting styles.

9. Why do the two yields differ?

They use different bases and different year lengths. Discount yield uses face value and 360 days. Investment yield uses price and 365 days. The investment figure therefore runs slightly higher.

10. What does price per hundred mean?

It restates your price per hundred of face. Paying 9,750 on 10,000 face gives 97.50. Dealers and newspapers quote prices this way. It helps you verify auction results quickly.

Practical Questions

11. Which yield should I compare with bank rates?

Use the investment yield for fair comparisons. Bank rates divide earnings by money deposited. The investment yield uses that same basis. Discount yield would flatter the bank unfairly.

12. Are Treasury bill profits taxed?

Federal income tax applies in the maturity year. State and local taxes never apply to bills. That exemption improves after tax returns notably. Keep your auction records for filing season.

13. Can I sell a bill before maturity?

Yes, bills trade actively in secondary markets daily. Your price then depends on current market rates. Rising rates can mean selling below expected value. Holding to maturity removes that uncertainty completely.

14. What happens if I enter price above face?

The calculator rejects that input with a warning. Bills always sell at a discount by design. A price above face signals a data error. Recheck your auction confirmation figures carefully then.

15. Do longer bills always yield more?

Usually longer terms pay slightly higher yields. Market conditions sometimes invert that pattern temporarily. Compare the investment yield at each maturity. Choose the term matching your cash timeline.

CONCLUSION

Treasury bills turn a simple discount into profit. The dollar return is just face minus price. Discount yield follows the old quoting tradition faithfully. Investment yield gives the fair, comparable annual figure. Our calculator produces all outputs from three inputs. Compare wisely, hold to maturity, and enjoy the safety.