Answer
$ 7\%$, compounded monthly
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=$ 7\%$, compounded monthly for 3 years:
$A=12,000(1+\displaystyle \frac{0.07}{12})^{12\cdot 3} \approx 14,795.11$
For r=$ 6.85\%$, compounded continuously for 3 years:
$A=12,000e^{0.0685\cdot 3}\approx 14,737.67$
7$\%$ compounded monthly yields the greater return.
