Answer
Monthly compounding at $ 7\%$ yields the greater return.
Work Step by Step
After t years, the balance, A, in an account with principal P and annual interest rate r (in decimal form), if compounded n times per year, is: $\displaystyle \quad A=P(1+\frac{r}{n})^{nt}$
if compounded continuously, it is: $\quad A=Pe^{rt}$
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Monthly compounding (n=12) at $ 7\%$: $\quad $
$ A=14,000(1+\displaystyle \frac{0.07}{12})^{12(10)}=28,135.26$
Continuous, at $ 6.85\%$
$ A=14,000e^{0.0685(10)}=27,772.81$
Monthly compounding at $ 7\%$ yields the greater return.
