91Ó°ÊÓ

Let us first name A gives 8% compounded semi-annually and B gives 7.9% compounded daily.

For A,

The rate of interest,$r=8\%=0.08$

The investment compounded semi-annually,$n=2$

For B,

The rate of interest,$r=7.9\%=0.079$

The investment compounded daily, $n=365$

The effective rate of interest $r_c$of an investment earning an annual interest rate $r$compounding $n$times per year is given by $r_c={\left(1+\frac{r}{n}\right)}^n-1$

Substitute the values of A in the effective rate of interest formula,

$$\begin{gathered} r_c={\left(1+\frac{0.08}{2}\right)}^2-1 \\ {r}_c={\left(1.04\right)}^2-1 \\ {r}_c=1.0816-1 \\ {r}_c=0.0816 \\ {r}_c=8.16\% \end{gathered}$$

Substitute the values of B in the effective rate of interest formula,

$$\begin{gathered} r_c={\left(1+\frac{0.079}{365}\right)}^{365}-1 \\ {r}_c={\left(1.00021\right)}^{365}-1 \\ {r}_c=1.08219-1 \\ {r}_c=0.08219 \\ {r}_c=8.219\% \end{gathered}$$

The effective rate of interest is the highest for B, so 7.9% compounded daily is a better deal.