Answer
The $8.25\%,$ compounded quarterly investment yields the greater return.
Work Step by Step
Semiannual compounding, $ t=4,\quad r=0.0825,\quad n=2$:
$ A=6000(1+\displaystyle \frac{0.0825}{4})^{4(4)}= {{\$}} 8317.84$
Quarterly compounding, $ t=4,\quad r=0.083,\quad n=4$:
$ A=6000(1+\displaystyle \frac{0.083}{2})^{2(4)}={{\$}} 8306.64$
The $8.25\%,$ compounded quarterly investment yields the greater return.
