A royalty contract promises a $$500,000$ sign$-$up bonus; ten annual royalty payments, starting with $$250,000,$ next year then growing at a rate of $6\mathrm{.}5\%$; and a final bonus $($in year ten, together with the last regular payment$)$ of $$800,000.$ If the appropriate discount rate is $10\mathrm{.}8\%,$ what is the value of all the payments if this royalty contract is signed today? Use the annuity formula in some of your calculations!