Sheridan Cosmetics Co$.$ purchased machinery on December $31,2024,$ paying $$51,500\mathrm{.}00$ down and agreeing to pay the balance in four equal installments of $$52,800\mathrm{.}00$ payable each December $31.$ An assumed interest of $10\%$ is implicit in the purchase price.

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Prepare the journal entries that would be recorded for the purchase and for $(1)$ the payments and $(2)$ interest on the following dates. $($Round present value factor to $5$ decimal places, e$.$g$.1\mathrm{.}23465$ and final answers to $2$ decimal places, e$.$g$.38,548\mathrm{.}23.$ If no entry is required, select $"$No Entry" for the account titles and enter $0$ for the amounts. Credit account titles are automatically indented when the amount is entered. Do not indent manually. List all debit entries before credit entries.$)$

$($a$)$ December $31,2024.$

$($b$)$ December $31,2025.$

$($c$)$ December $31,2026.$

$($d$)$ December $31,2027.$

$($e$)$ December $31,2028.$