Your brother$-$in$-$law asks you to lend him $$200000\mathrm{.}00$ as a second mortgage on his vacation home. He promises to make level monthly payments for $10$ years, $120$ payments in all. You decide that a fair interest rate is $6\mathrm{.}00\%$ compounded annually. What should the monthly payment be on the $$200000\mathrm{.}00$ loan?

$$2220\mathrm{.}41$

$$1766\mathrm{.}67$

$$2264\mathrm{.}47$

$$2168\mathrm{.}14$

$$1666\mathrm{.}67$