Treasury Bills, Yield Curves, and Simple Interest: How Short-Term Government Debt is Priced

Treasury bills are priced using simple interest — and understanding how explains how short-term government debt markets work

Treasury bills (T-bills) are short-term government securities with maturities of weeks to one year. They're the safest liquid investment available in most countries — backed by the full faith and credit of the government. And unlike bonds, which pay periodic coupon interest, T-bills use a discount pricing model that is essentially simple interest applied in a specific way.

Understanding how T-bills are priced also explains how money market rates, commercial paper, and short-term credit markets work — all of which use the same discount yield framework.

Simple interest: the foundation

Simple interest accrues only on the principal — it doesn't compound. The formula:

Interest = Principal × Rate × Time

Where Time is expressed as a fraction of a year (days ÷ day count basis).

Example: £10,000 at 5% for 90 days (using 365-day year): Interest = £10,000 × 0.05 × (90/365) = £123.29 Maturity value = £10,123.29

This simple interest calculation is the foundation of T-bill pricing.

How T-bills are priced: the discount model

T-bills are sold at a discount to their face value. You pay less than £100 today; at maturity, you receive £100. The difference is the interest.

Discount rate vs. yield:

The discount rate is quoted as a percentage of the face value (not the purchase price): Discount = Face value × Discount rate × (Days to maturity / Day count basis)

UK T-bill example: Face value: £100 Discount rate: 4.8% Term: 91 days Day count basis: 365 (UK convention)

Discount = £100 × 0.048 × (91/365) = £1.196 Purchase price = £100 − £1.196 = £98.804

If you invest £98.804 and receive £100 in 91 days, your actual return on investment:

Yield = (Discount / Purchase price) × (365 / Days) × 100 = (£1.196 / £98.804) × (365/91) × 100 = 4.85%

This is slightly higher than the 4.8% discount rate — because you earned £1.196 on a £98.804 investment, not on the £100 face value.

US T-bills use a 360-day year (bank discount basis), while UK gilts and most other markets use 365 days. This produces slightly different effective yields for the same nominal rate.

Yield curves and what they tell you

Government bonds and T-bills of different maturities together form the yield curve — a plot of yield (vertical) against maturity (horizontal).

Normal yield curve (upward sloping): longer maturities have higher yields. Investors demand more return for locking money away longer (liquidity premium) and for taking on more duration risk (if rates rise, long-term bonds fall in price more than short-term).

Inverted yield curve: shorter maturities have higher yields than longer maturities. This occurred in the US and UK from 2022–2024 when short-term rates were aggressively raised to fight inflation. An inverted yield curve has historically preceded recessions in many economies.

Flat yield curve: similar yields across maturities — typically transitional between normal and inverted.

The 2-year/10-year spread: the most watched yield curve relationship. When the 2-year Treasury yield exceeds the 10-year Treasury yield (inversion), the spread is negative. The 2s10s spread inverted in March 2022 and remained inverted through 2024 — the longest inversion since the early 1980s.

Real yield vs. nominal yield

A government bond paying 4% when inflation is 3% provides a 1% real yield — your purchasing power grows by only 1% per year despite the 4% nominal return.

UK Index-linked gilts (linkers): face value and coupon payments are adjusted for the Retail Price Index (RPI). The coupon is a real yield — the total return is the real coupon plus inflation.

US Treasury Inflation-Protected Securities (TIPS): principal adjusted for CPI. A 10-year TIPS at 1.5% real yield guarantees 1.5% above inflation over 10 years, regardless of what inflation does.

When you see financial headlines about "real yields turning positive," it means the nominal government bond yield has risen above the current inflation rate — representing genuine positive real return for bond holders.

How simple interest applies to personal loans and credit

Beyond government securities, simple interest applies to various consumer financial products:

Bank overdrafts: typically calculated on daily outstanding balance × daily rate × days. If your overdraft rate is 39.9% EAR, the daily rate is approximately 0.093%. An overdraft of £500 for 10 days: Simple interest = £500 × 0.00093 × 10 = £4.65

Car hire purchase (flat rate): some car finance products quote a flat (simple) rate. As covered in the loan planner post, a 10% flat rate ≈ 18% APR — the flat rate applies to the original principal throughout, not the reducing balance.

Invoice financing / trade credit: "2/10 net 30" is a common business payment term meaning "take 2% discount if you pay in 10 days, otherwise pay full price in 30 days." The annualised cost of not taking the discount: = (2% / 98%) × (365 / (30-10)) = 37.2% per year

This is the return a supplier earns if you take the discount, or the cost of credit if you don't — expressed as a simple interest annualised rate.

Compound vs. simple interest: when the difference matters

For periods under one year, the difference between simple and compound interest is small. For longer periods, the difference compounds.

£10,000 at 5% over 10 years:

• Simple interest: £10,000 + (£10,000 × 0.05 × 10) = £15,000
• Annual compound interest: £10,000 × (1.05)¹⁰ = £16,288

The £1,288 difference represents the interest earned on interest over 10 years.

For T-bills and short-term instruments (under 1 year), simple interest is the conventional calculation because the difference from compound interest is negligible and the calculation is simpler for markets that need to quote consistent rates across different maturities.

How to use the Simple Interest Calculator on sadiqbd.com

1. Enter principal, rate, and time period
2. Calculate interest and total amount
3. Use for:
   • T-bill yield calculations (compare discount rate to effective yield)
   • Overdraft cost estimation
   • Trade credit cost analysis ("is it worth taking the early payment discount?")
   • Car loan flat rate to APR comparison

Frequently Asked Questions

Is T-bill interest taxable? In most countries, T-bill interest (the discount earned) is taxable as income. In the UK, gilt interest is subject to income tax (not Capital Gains Tax). In the US, Treasury interest is subject to federal income tax but exempt from state and local income taxes — a small advantage over corporate bonds or savings accounts that are subject to all three levels.

Can individual investors buy T-bills directly? Yes — the UK sells gilts directly through the DMO; US Treasuries are available at TreasuryDirect.gov with no broker fees; Australian government bonds through CommSec or Westpac. Alternatively, money market funds invest heavily in T-bills and provide equivalent exposure with daily liquidity.

Is the Simple Interest Calculator free? Yes — completely free, no sign-up required.

Simple interest underlies the pricing of the safest assets in the financial system — government T-bills — and connects to familiar consumer products from overdrafts to flat-rate car loans. Understanding the discount yield formula and the difference between nominal and real yields turns abstract financial news into comprehensible information about how capital markets are functioning.

Try the Simple Interest Calculator free at sadiqbd.com — calculate interest, total amount, and time for any principal, rate, and term combination.