Jan sold her house on December $31$ and took a $$30,000$ mortgage as part of the payment. The $10-$year mortgage has a $10\%$ nominal interest rate, but it calls for semiannual payments beginning next June $30.$ Next year Jan must report on Schedule B of her IRS Form $1040$ the amount of interest that was included in the two payments she received during the year.

a$.$ What is the dollar amount of each payment Jan receives? Round your answer to the nearest cent. $

b$.$ How much interest was included in the first payment? Round your answer to the nearest cent. $

b$\mathrm{.}2$ How much repayment of principal was included? Do not round intermediate calculations. Round your answer to the nearest cent. $

c$.$ How much interest must Jan report on Schedule B for the first year? Do not round intermediate calculations. Round your answer to the nearest cent. $$3,000\mathrm{.}00($correct according to $$Check my work.$)$