Diana is $15$ years old. She plans on working each of the next three summers, as a lifeguard, and intends to contribute $$3,000$ of her lifeguard earnings each year into her Roth IRA. She plans to allocate $100\%$ of these contributions into an S&P $500$ index fund, with a long$-$term, net$-$of$-$fee expected rate of return of $10\mathrm{.}0\%.$

Assume that Diana is $16$ years old when she makes her first contribution, $17$ years old when she makes her second, and $18$ years old when she makes her third. What is the estimated Future Value of Diana$$s lifeguarding contributions at Age $60,$ after taxes? Use annual compounding. Assume the capital gains tax rate is $20\%.$

$(1$ Point$)$

$$436,843$

$$543,804$

$$1,592,738$

$$1,957,922$