Jazelle Momba wants to visit her family in Zimbabwe in $2022,$ which is $6$ years from now. She knows that it will cost approximately $$7,700$ including flight costs, on$-$the$-$ground costs, and extra spending money to stay for $4$ months. If she opens an account that compounds interest at $4\%$ semiannually, how much does she need to deposit today to cover the total cost of her visit?