You purchase a plot of land worth $$54,000$ to create a community garden. To do so$,$ you secure a $10-$year loan, charging $5\mathrm{.}66\%$ APR, compounded monthly, and requiring monthly payments of $$505.($Assume the value of the land is still $$54,000.$ Round each answer to the nearest dollar.$)$

$($a$)$Assuming that you put some money down, what was your original loan amount $($in dollars$)?$

$

$($b$)$What is the outstanding balance $($in dollars$)$ on your loan after making $4$ years of payments?

$

$($c$)$How much equity $($in dollars$)$ do you have in the garden after $4$ years?

$