On January $1,2024,$ Stoops Entertainment purchases a building for $$520,000,$ paying $$110,000$ down and borrowing the remaining $$410,000,$ signing a$($n$)9\%,20-$year mortgage. Installment payments of $$3,688\mathrm{.}88$ are due at the end of each month, with the first payment due on January $31,2024.$

$4.$ Total payments over the $20$ years are $$885,331($$$3,688\mathrm{.}88240$ monthly payments$).$ How much of this is interest expense and how much is actual payment of the loan? $($Round your final answers to the nearest whole dollar amount.$)$

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$3-$a$.$ Record the first monthly mortgage payment on January $31,2024.$

$3-$b$.$ How much of the first payment goes to interest expense and how much goes to reducing the carrying value of the loan?