Introduction
Treasury Bills, or T-Bills, are short-term zero-coupon securities issued by the Government of India.
They are presently issued in three standard tenors:
91 days;
182 days; and
364 days.
A T-Bill does not pay periodic interest. It is purchased at a price below its face value and redeemed at face value on maturity. The difference represents the investor's return. RBI describes T-Bills on this discount-and-redemption basis.
This makes T-Bill numericals different from coupon-bearing bond calculations.
For CAIIB, the important relationships are:
Face Value → Discount → Purchase Price → Holding Period → Yield
The 2026 IIBF syllabus includes Money Market Products and Securities Market Products within BFM Module C, Treasury Products. IIBF also specifically states that CAIIB may contain numerical questions where candidates must key in the answer without MCQ options.
Learning Objectives
After studying this topic, you should be able to:
understand how T-Bill price and discount are related;
calculate the discount from face value and purchase price;
understand the annualised yield calculation used for T-Bills;
derive price when yield and tenor are given;
distinguish investment yield from discount rate;
apply the actual/365 money-market convention; and
avoid common numerical errors in CAIIB questions.
Basic T-Bill Calculation Logic
A Treasury Bill has only two basic cash flows from an investor's point of view:
Purchase: investor pays less than face value.
Maturity: investor receives the face value.
There is no intermediate coupon.
Therefore, the investor's return comes entirely from the difference between:
maturity value; and
purchase price.
This simplicity makes T-Bill numericals relatively easy once the correct denominator and day-count convention are understood.
Face Value, Price and Discount
Face Value
Face value is the amount payable by the Government on maturity.
Government securities in India are generally quoted with reference to ₹100 face value. RBI describes face value as the amount repaid to the investor at maturity.
Purchase Price
Purchase price is the amount paid by the investor to acquire the T-Bill.
Because T-Bills are normally issued at a discount:
Purchase Price < Face Value
Discount
The discount is the difference between face value and purchase price.
Discount = Face Value − Purchase Price
This formula calculates the rupee amount of discount embedded in the T-Bill price.
Refer to the Formula Section for a detailed explanation, variables, and solved examples.
Understanding Price Quotation
Suppose a T-Bill is quoted at a price below ₹100.
The quotation tells us how much must be paid for ₹100 face value.
A lower quoted price means:
a larger discount;
a larger maturity gain; and
generally a higher yield, other things remaining unchanged.
A higher quoted price means:
a smaller discount;
a smaller maturity gain; and
generally a lower yield.
Therefore:
Price ↑ → Yield ↓
Price ↓ → Yield ↑
This inverse relationship is one of the most important T-Bill concepts for CAIIB.
Day-Count Convention
The day-count convention determines how the holding period is annualised.
RBI states that the Indian money market uses the actual/365 convention.
This means:
use the actual number of days for the relevant T-Bill period; and
use 365 days as the annual base.
RBI specifically notes that T-Bills are money-market instruments and therefore follow the money-market convention of actual/365.
T-Bill Yield
The T-Bill yield measures the annualised return earned relative to the amount actually invested.
T-Bill Yield (%) = [(Face Value − Purchase Price) ÷ Purchase Price] × [365 ÷ Days to Maturity] × 100
This converts the return earned on the purchase price during the remaining tenor into an annual percentage rate using actual/365.
Refer to the Formula Section for a detailed explanation, variables, and solved examples.
RBI's Government Securities primer specifically provides a T-Bill yield calculation after confirming that T-Bills follow the money-market day-count convention.
Why Is Purchase Price Used in the Denominator?
An investor does not invest the face value.
The investor actually pays the purchase price.
Therefore, when measuring the return earned on the money invested, the return is related to purchase price.
This point is important because another measure—the discount rate—uses face value as the denominator.
Confusing these denominators produces a wrong answer.
Annualised Discount Rate
A T-Bill discount can also be expressed as an annualised percentage of face value.
Annualised Discount Rate (%) = [(Face Value − Purchase Price) ÷ Face Value] × [365 ÷ Days to Maturity] × 100
This measures the annualised discount relative to face value rather than the amount actually invested.
Refer to the Formula Section for a detailed explanation, variables, and solved examples.
Yield and Discount Rate Are Not the Same
This distinction is highly exam-relevant.
Basis | T-Bill Yield | Discount Rate |
|---|---|---|
Return/discount amount | Face Value − Price | Face Value − Price |
Main denominator | Purchase Price | Face Value |
Annualisation | Actual/365 | Actual/365 |
Relative size | Normally higher | Normally lower |
Reason | Price is below face value | Face value is larger denominator |
Because a normal T-Bill price is below its face value:
Purchase Price < Face Value
Therefore, for the same instrument:
Investment Yield > Discount Rate
Calculating T-Bill Price from Yield
CAIIB may reverse the question.
Instead of giving price and asking for yield, it may provide:
face value;
yield; and
remaining days to maturity.
The required value is then the T-Bill price.
Purchase Price = Face Value ÷ [1 + {(Yield ÷ 100) × (Days to Maturity ÷ 365)}]
This rearranges the investment-yield relationship to determine the price corresponding to a given annualised yield and tenor.
Refer to the Formula Section for a detailed explanation, variables, and solved examples.
Reasonableness Check
For an ordinary positive-yield T-Bill:
Purchase Price should be below Face Value.
If your calculation produces a price above face value in a conventional positive-yield question, recheck:
denominator;
percentage conversion;
number of days; and
placement of 365.
Calculating Price from a Discount Rate
Where the question specifically gives an annualised discount rate rather than investment yield, price is derived from the discount applied to face value.
Purchase Price = Face Value × [1 − {(Discount Rate ÷ 100) × (Days to Maturity ÷ 365)}]
This calculates the price where the quoted rate is expressly a face-value-based discount rate.
Refer to the Formula Section for a detailed explanation, variables, and solved examples.
This formula should not be substituted for the investment-yield formula unless the question actually gives a discount rate.
Why Yield and Price Move in Opposite Directions
A Treasury Bill redeems at a fixed face value.
Suppose market yields rise.
A new investor will require a greater return.
Because the maturity amount remains fixed, the investor must acquire the T-Bill at a lower price to obtain that higher return.
Therefore:
Yield ↑ → Price ↓
Conversely:
Yield ↓ → Price ↑
RBI similarly explains the general inverse relationship between security price and market yield.
Effect of Tenor on the Calculation
Time is an essential part of a T-Bill numerical.
The same rupee discount earned over:
91 days; and
364 days
does not represent the same annualised return.
If the same gain is earned in a shorter period, the annualised yield is higher.
Therefore, do not compare two T-Bills merely by looking at their rupee discount.
You must consider:
Return + Price + Time
Original Maturity vs Remaining Maturity
Another possible calculation trap is confusing:
original tenor of the T-Bill; and
remaining days to maturity on the purchase or settlement date.
If an investor buys a T-Bill in the secondary market after it has already been outstanding for some time, the relevant yield calculation is based on the remaining period to maturity, not automatically its original 91-day, 182-day, or 364-day tenor.
This is important in secondary-market calculations.
Primary Auction Price and Yield
In a competitive T-Bill auction, bidders may quote the required price or yield according to the auction framework.
RBI publishes auction results containing:
cut-off price;
cut-off yield;
weighted average price; and
weighted average yield.
For example, RBI's published T-Bill auction results show separate price and YTM figures for 91-day, 182-day, and 364-day securities.
The relationship remains:
higher acceptable price → lower corresponding yield
and
lower acceptable price → higher corresponding yield.
Cut-Off Price vs Weighted Average Price
These terms should not be confused.
Cut-Off Price
The cut-off represents the auction boundary determined through competitive bidding.
Bids outside the acceptable auction range are not successful.
Weighted Average Price
This is the average of accepted competitive prices after weighting each price by the amount accepted at that price.
Non-competitive allotment is linked to the applicable weighted-average auction result under the prevailing framework.
For a numerical question, always identify whether the question asks for:
individual bid price;
cut-off price;
weighted average price; or
yield corresponding to a price.
Calculation Decision Process
Before touching the calculator, identify what the question gives and what it asks.
If Face Value and Price Are Given
First identify the discount.
Then check whether the question asks for:
simple discount;
annualised discount rate; or
T-Bill yield.
If Face Value, Yield and Days Are Given
Find the price using the yield-based price relationship.
If Face Value, Discount Rate and Days Are Given
Find price using the face-value-based discount relationship.
If Price and Yield Direction Are Asked
Use the inverse relationship:
Yield rises → Price falls
Yield falls → Price rises
Calculator Discipline for CAIIB
T-Bill numericals are usually short, but small arithmetic mistakes can change the answer.
Use the following sequence mentally:
1. Identify what is given.
Check:
face value;
price;
tenor or remaining days;
yield; or
discount rate.
2. Identify what is required.
Do not calculate yield when the question asks for discount rate.
3. Check the denominator.
This is one of the most important steps.
Yield → Purchase Price
Discount Rate → Face Value
4. Use actual/365.
Do not substitute another day-count basis unless the question explicitly requires it.
5. Convert percentage correctly.
A percentage used inside an equation may need conversion from percentage form to decimal form.
6. Check the direction of the answer.
Higher yield should correspond to lower price.
7. Apply sensible rounding only at the end.
Avoid repeatedly rounding intermediate numbers because that may create an avoidable final difference.
CAIIB Exam Focus
T-Bills are zero-coupon instruments.
There is no periodic coupon to add to the return.
Return arises from discount.
The investor buys below face value and receives face value on maturity.
Indian T-Bill calculations use the money-market actual/365 convention.
T-Bill yield uses purchase price as the denominator.
This measures return on the amount actually invested.
Discount rate uses face value as the denominator.
Do not confuse it with investment yield.
Yield is normally higher than the corresponding discount rate.
This follows because purchase price is below face value.
Price and yield move inversely.
This is fundamental.
Use remaining maturity where relevant.
A secondary-market transaction may not have the full original tenor remaining.
Read “yield” and “discount rate” carefully.
They are not interchangeable.
Numerical answers may need to be entered directly in CAIIB.
The current IIBF examination rules expressly permit numerical questions without answer options.
Common Exam Traps
Trap 1: Treating Discount as Coupon Interest
Incorrect.
T-Bills have no periodic coupon. Their return is generated through the difference between purchase price and maturity value.
Trap 2: Using Face Value as the Denominator for T-Bill Yield
Incorrect.
For the investment-yield calculation, the denominator is the amount invested—the purchase price.
Trap 3: Using Purchase Price for Discount Rate
Incorrect.
The conventional discount-rate calculation uses face value.
Trap 4: Assuming Yield and Discount Rate Must Be Equal
Incorrect.
They use different denominators.
Trap 5: Using 360 Days Automatically
Incorrect for the RBI-described Indian T-Bill money-market convention.
Use actual/365.
Trap 6: Using Original Maturity in Every Question
Incorrect.
When a T-Bill is purchased after issue, the calculation may require the remaining days to maturity.
Trap 7: Assuming Higher Price Means Higher Yield
Incorrect.
T-Bill price and yield move inversely.
Trap 8: Forgetting Annualisation
A return earned over 91 or 182 days cannot simply be presented as an annual yield without adjusting for time.
Trap 9: Treating 5% as 5 Inside a Decimal Calculation
This can produce a very large error.
Read the percentage format carefully before substitution.
Trap 10: Rounding Too Early
Repeated rounding can create an incorrect final answer, especially when the examination expects a specific numerical value.
Memory Technique
Remember P-D-Y:
P – Price: amount actually paid
D – Discount: Face Value minus Price
Y – Yield: return measured on Price and annualised
For the two denominators, remember:
Y = Your money invested → Price
D = Discount from denomination → Face Value
And for market movement:
Yield UP → Price DOWN