Celesta Frank wants to go on a cruise in three years. She could earn $8\mathrm{.}2$ percent compounded monthly in an account if she deposits the money today. She needs to have $$10,000$ in three years. How much will she have to deposit today? $($Round to the nearest dollar.$)$

$$6,432$

$$7,826$

$$8,148$

$$7,763$