Answer
$ r\approx 0.2503\%$
Work Step by Step
The annual yield of a T-bill is the simple annual interest rate an investor earns when the T-bill matures
A T-Bill (costing PV$=?$ dollars),
at the the end of its life (of t$=0.5$ years)
pays the maturity (FV$=5000$)
at discount rate $r=0.0025$, meaning that
$PV=FV(1-rt)=5000(1-0.0025\cdot 0.5)=4993.75$
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So, investing $PV=4993.75$ for t=$0.5$ years
yields $FV=5000$. In simple interest terms,
$INT=FV-PV=6.25$, and
$FV=PV(1+rt)$, which we sove for r:
$FV=PV+PVrt\qquad /-PV$
$FV-PV=PVrt\qquad/\div(PV\cdot t)$
$ r=\displaystyle \frac{6.25}{PV\cdot t}=\frac{6.25}{4993.75\cdot 0.5}\approx$0.00250312891114
$ r\approx 0.2503\%$
