Question:
Sue can either borrow $10,\!000$ dollars for $5$ years with a simple interest of $7\%$ annually or an interest which compounds annually for $6\%$. How much more money, rounded to the nearest dollar, would she have to pay back for the more expensive interest than the less expensive interest?

Answer:
For the simple interest rate, she would have to pay an interest of $10000 \cdot 0.07=700$ dollars every year. Since there are $5$ years, in the end she would have to pay back $10000+5\cdot 700=13500$ dollars.

For the compounded interest, her balance is multiplied by $1+6\%=1.06$ each year. Therefore, at the end of 5 years her balance is $A=10000(1+0.06)^5=13382.255..$.

The simple interest rate would be more expensive by $13500-13382.255 \approx \boxed{118 \text{ dollars}}$.