91Ó°ÊÓ

Let us first name A gives 9% compounded monthly and B gives 8.8% compounded daily.

For A,

The rate of interest, $r=9\%=0.09$

The investment compounded monthly, $n=12$

For B,

The rate of interest, $r=8.8\%=0.088$

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,

$$\begin{gathered} r_c={\left(1+\frac{0.09}{12}\right)}^{12}-1 \\ {r}_c={\left(1.0075\right)}^{12}-1 \\ {r}_c=1.09380-1 \\ {r}_c=0.09380 \\ {r}_c=9.380\% \end{gathered}$$

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

$$\begin{gathered} r_c={\left(1+\frac{0.088}{365}\right)}^{365}-1 \\ {r}_c={\left(1.00024\right)}^{365}-1 \\ {r}_c=1.09197-1 \\ {r}_c=0.09197 \\ {r}_c=9.197\% \end{gathered}$$

The effective rate of interest is highest for A, so 9% compounded monthly is a better deal.