What is the difference in future value between investments that earn $8\mathrm{.}2\%$ APR $($monthly compounded$)$ and $7\mathrm{.}1\%$ APR $($monthly compounded$)$ over $40$ years, assuming I put $$550$ in each account each month, and the interest is compounded monthly? Round your answer to the nearest thousand dollar.

Hint: Calculate the values of each investment, and subtract the larger from the smaller.

Question $14$ options:

$$433,000$

$$549,000$

$$1,745,000$

$$58,000$

$$23,000$

none of these

$$97,000$