Remember that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
In the 3.99% compounded semiannually
we have
r=3.99%=0.0399
n=2
substitute
[tex]\begin{gathered} A=P(1+\frac{0.0399}{2})^{2t} \\ \\ A=P(1.01995)^{2t} \end{gathered}[/tex]
and
[tex]\begin{gathered} A=P[(1.01995)^2]^t \\ A=P(1.0403)^t \end{gathered}[/tex]
the rate is r=1.0403-1=0.0403=4.03%
In the 3.8% compounded quarterly
we have
r=3.8%=0.038
n=4
substitute
[tex]\begin{gathered} A=P(1+\frac{0.038}{4})^{2t} \\ A=P(1.0095)^{2t} \\ A=P[(1.0095)^2]^t \\ A=P(1.0191)^t \end{gathered}[/tex]
the rate is r=1.0191-1=0.0191=1.91%
therefore
the 3.99% compounded semiannually is a better investment
