You are trying to decide how much money to put away to cover future expenses. You currently have $2,164$ dollars in your savings account. You expect the following cash flows at the end of the relevant years: an expense of $3,254$ dollars three years from now, an expense of $6,262$ dollars seven years from now, and both an inflow of $3,933$ dollars and outflow of $7,148$ dollars $8$ years from now. How much money do you need to deposit today in order to honor these future financial obligations if your savings account yields $4\%$ per year? Only a single deposit today is allowed; no other option available. $($note: round your answer to the nearest cent, and do not include spaces, currency signs, plus or minus signs, or commas$)$