Juan provides a loan in the amount of $$200,000$ to his daughter, Imelda, on January $1,2023.$ The loan is still outstanding on December $31,2023.$ The Federal rate applicable to the loan is $4\mathrm{.}2\%$ through June $30$ and $4\mathrm{.}75\%$ from July to December $31.$ How much imputed interest income must Juan recognize for tax year $2023?$

$8,400$

$9,700$

$9,050$

None of the answers are correct.