Assume that under a privatized Social Security System you would have a choice of mutual funds in which to invest your FICA taxes, just like you do in a $401-$K$.$ Assume that you are $27-$years$-$old and plan to retire in $40$ years. You currently earn $$85,000$ a year, and earnings are expected to increase at a $4\mathrm{.}5\%$ annual rate.

$1.$ What is the total amount that you will pay in FICA taxes during your worklife, if the FICA tax rate is $12\mathrm{.}4\%$ and if only the first $$160,200$ of income is taxed. Please note that currently the employee pays $6\mathrm{.}2\%$ and the employer pays $6\mathrm{.}2\%.$ Any way you look at it$,$ you contribute to you Social Security account $12\mathrm{.}4\%$ of your income up to $$160,200.$

$2.$ How much money would your SS account hold at age $67$ if your contributions had been invested in an S&P $500$ index fund with an average annual rate of return of $11\mathrm{.}5\%?$