How is the price of US T-Bill's calculated here on CNBC?

Question

https://www.cnbc.com/quotes/US6M

Here, the price is given (as of the time of asking) as 5.285, and it is not clear to me how the yield and price here are exactly related. It is clear for me however, how it is done for T-Bonds, using the following formula

$$ \begin{align} P &= \begin{matrix} \left(\frac{C}{1+i}+\frac{C}{(1+i)^2}+ ... +\frac{C}{(1+i)^N}\right) + \frac{M}{(1+i)^N} \end{matrix}\\ &= \begin{matrix} \left(\sum_{n=1}^N\frac{C}{(1+i)^n}\right) + \frac{M}{(1+i)^N} \end{matrix}\\ &= \begin{matrix} C\left(\frac{1-(1+i)^{-N}}{i}\right)+M(1+i)^{-N} \end{matrix} \end{align} $$

as given on https://en.wikipedia.org/wiki/Bond_valuation page on Wikipedia. I cannot see how to use this formula for T-Bills where coupon is zero.

Answer 1

T-Bill's follow the discount rate methodology outlined by the U.S. Treasury in their document Price, Yield and Rate Calculations for a Treasury Bill here. What CNBC is displaying is the converted yield, i.e. you use the Discount Rate of 5.28% and then calculate the dollar price of the Bill

=100*(1-0.0528*182/360)

which gives approx 97.3. Next convert the price using the "Coupon Equivalent Yield" formula to get to the value displayed (5.515%):

=(100-97.3306667)/97.3306667*366/182*100

Note that 182 is the days to maturity (accounting for T+1 settlement from today).