Answer
$ r=3.775\%$
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$=\displaystyle \frac{6}{12}=0.5$ years)
pays the maturity (FV)
at discount rate $r=0.03705$, meaning that
$ PV=FV(1-rt)=FV\cdot$0.981475
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So, investing $ PV=FV\cdot$0.981475 for t=$0.5$ years
yields $FV$, and we want to know the simple annual rate r.
In simple interest terms,
$FV=PV(1+rt)$, which we sove for r:
$ FV=FV\cdot$0.981475$(1+0.5r)\quad /\div(FV\cdot$0.981475$)$
$\displaystyle \frac{1}{0.981475}=1+0.5r\qquad/-1$
$\displaystyle \frac{1}{0.981475}-1=0.5r\qquad/\times 2$
$ r=2(\displaystyle \frac{1}{0.981475}-1)\approx$0.0377493058916
to the nearest $0.001\%,$
$ r=3.775\%$
