A corporation creates a sinking fund in order to have $$510,000$ to replace some machinery in $12$ years. How much should be placed in this account at the end of each quarter if the annual interest rate is $6\mathrm{.}3\%$ compounded quarterly? $($Round your answers to the nearest cent.$)$

$

How much interest would they earn over the life of the account?

$

Determine the value of the fund after $2,4,$ and $6$ years.

$2$ years $

$4$ years $

$6$ years $

How much interest was earned during the fourth quarter of the $5$th year?

$