Jenny took out a loan for $$2,000$ with an annual effective rate of interest of $5\mathrm{.}8\%.$ She repays the loan with the following three payments:

a payment of $$475$ at the end of year $1,$

a payment of $$1,000$ at the end of year $3$ and

a final payment of X at the end of year $5.$

Find the outstanding loan balance at the end of year $1.($answer to the nearest cent$)$

Find the outstanding loan balance at the end of year $3.($answer to nearest cent$)$

Find the size of the final payment X$.($answer to the nearest cent$)$

Find the amount of interest in the last payment. $($answer to the nearest cent$)$