# How to use exp(-r*t) to calculate tbill price

I wonder why : $$1 - \left(\frac{4.91\% \times 358}{360}\right) = 95.1172778$$

and why $$\exp\left(-4.91\% \times \frac{358}{360}\right)$$ does not give 95.1172778

T Bill Description :

B 0 04/17/25 ( 912797KS5 )

Discount           4.91000
Settle             04/24/24
Price              95.1172778
Issue              04/18/2024
Days to Maturity   358
Maturity           04/17/2025


• I think you're just confused by the price quote convention used which is not the exact same value as the continuous yield. Commented Apr 23 at 15:40
• @DStanley Then which rate should I use to retrieve the correct price using exp(-rt) ? Thanks Commented Apr 23 at 15:42
• The price is the price. The quoted annualized yield will be different than the calculated continuous yield. Commented Apr 23 at 15:43
• @DStanley since Tbill is 0 coupon I except the discount factor to be the price so exp(-rt) should work ? Can you please clarify what is the "Discount Rate" and it's difference with UST Treasury Convention Yield ? Mathematical answer is more than welcome. Commented Apr 23 at 15:46
• Apply the correct formula for prices of Bills: P = 100 * (1 - 0.0491 * 359 /360). Assuming a continuously compounded rate is equal to the discount rate on a bill is an error, as explained.
– Attack68
Commented Apr 23 at 16:10

In order to calculate the actual continuous yield (e.g. r in exp(-r*t)) you have to decide how to calculate t which is where different conventions come into play. In academics, t is generally given and is a fraction or multiple of a year (e.g. 1 or 0.5 or 2). In reality, what is t for a bond that matures in 358 calendar days? Is it 358/365? should you only consider trading days instead of calendar days? This is where different quoting conventions come into play.