A loan of $$7,000$ is repaid over $12$ years using one of the following two methods:

Amortization with annual end of year payments based on an annual effective rate of $6\mathrm{.}5\%.$

The sink fund method, where the borrower pays the lender interest at rate i at the end of each year. The borrower also makes end of year deposits into a sinking fund earning an annual effective rate of $4\mathrm{.}5\%$ to repay the principal in $12$ years.

Find the annual amortization payment to the nearest cent.

Find the sink fund deposit to the nearest cent.

Find the rate of interest i that will make both repayment methods have the same annual cost. $($Give your answer in decimal format to $4$ decimal places$)$