jmc

She would get $20000\cdot 0.06=1200$ dollars per year from the simple interest. This gives her $20000+4\cdot 1200=24800$ dollars in the end.

For the compounded interest, we use the formula $A=P{\left(1+\frac{r}{n}\right)}^{nt}$, where $A$ is the end balance, $P$ is the principal, $r$ is the interest rate, $t$ is the number of years, and $n$ is the number of times compounded in a year. This equation represents the idea that the interest is compounded every $1/n$ years with a rate of $r/n$ each time. Substituting the information given, we get $$A=20000{\left(1+\frac{0.07}{4}\right)}^{4\cdot 4}=20000{\left(1+\frac{0.07}{4}\right)}^{16}\approx 26399.$$Therefore, she should choose the compounded interest and earn $26399-24800=\boxed{1599\text{ dollars}}$ more.