Consider an installment loan of $$25,000$ at an annual interest rate of $6\%$ to be paid back over $4$ years. The loan interest compounds monthly, and payments are also due monthly.

$($b$)$ Suppose the borrower decides to make an additional payment of $$100$ each month specifically towards the principal. Calculate how much sooner the loan would be paid off with these extra payments.

$($c$)$ Determine the total amount of interest saved by making these additional principal payments.