Today is Janet's $23$rd birthday. Starting today, Janet plans to begin saving for her retirement. Her plan is to contribute $$1,000$ to a brokerage account each year on her birthday. Her first contribution will take place today. Her $42$nd and final contribution will take place on her $64$th birthday. Her aunt has decided to help Janet with her savings, which is why she gave Janet $$10,000$ today as a birthday present to help get her account started. Assume that the account has an expected annual return of $10$ percent. How much will Janet expect to have in her account on her $65$th birthday? The answer is $$1,139,037\mathrm{.}68.$ Please show me the work for an understanding.