Answer
$ 8.25\%$, compounded quarterly
Work Step by Step
After $t$ years, the balance, $A$,
in an account with principal $P$
and annual interest rate $r$ (in decimal form)
is given by one of the following formulas:
1. For $n$ compoundings per year: $A=P(1+\displaystyle \frac{r}{n})^{nt}$
2. For continuous compounding: $A=Pe^{rt}$.
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For r=$ 8.25\%$, compounded quarterly (n=4) for t=4 years:
$ A=6000(1+\displaystyle \frac{0.0825}{4})^{4\cdot 4}\approx \$ 8317.84$
For r=$ 8.3\%$, compounded semiannually (n=2) for t=4 years:
$A=6000(1+\displaystyle \frac{0.083}{2})^{2\cdot 4}\approx\$ 8306.64$
8.25$\%$, compounded quarterly yields the greater return.