91Ó°ÊÓ

Let us first name A gives 6% compounded quarterly and B gives $6\frac{1}{4}\%$compounded annually.

For A,

The rate of interest, $r=6\%=0.06$

The investment compounded quarterly,$n=4$

For B,

The rate of interest, $r=6\frac{1}{4}\%=\frac{25}{4}\%=0.0625$

The investment compounded annually,$n=1$

The effective rate of interest $r_c$of an investment earning an annual interest rate $r$compounding $n$times per year is given by,role="math" localid="1647117616811" $r_c={\left(1+\frac{r}{n}\right)}^n-1$

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

$$\begin{gathered} r_c={\left(1+\frac{0.06}{4}\right)}^4-1 \\ {r}_c={\left(1.015\right)}^4-1 \\ {r}_c=1.06136-1 \\ {r}_c=0.06136 \\ {r}_c=6.136\% \end{gathered}$$

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

$$\begin{gathered} r_c={\left(1+\frac{0.0625}{1}\right)}^1-1 \\ {r}_c=\left(1.0625\right)-1 \\ {r}_c=0.0625 \\ {r}_c=6.25\% \end{gathered}$$

The effective rate of interest is highest for B, so $6\frac{1}{4}\%$compounded annually is the better deal.