Suppose that you inherit $$100,000$ and invest it until you retire $30$ years from now, in a fund that averages $7\mathrm{.}5\%$ annual earnings, which you reinvest. $($Round your answers to the nearest cent.$)$

$($a$)$ How much will you have at the end of the $30$ years?

$

$($b$)$ Managers of investment funds usually charge a percentage each year of the amount invested $($even if the investments lose moneyl$).$ Suppose that the investment fund management charges you $0\mathrm{.}25\%,$ so you earn $7\mathrm{.}25\%$ instead of $7\mathrm{.}5\%.$ How much will you have at the end of the $30$ years?

$