On January $2,2022,$ a company purchased a piece of equipment to be used in its operations. The price of the machine is to be paid in four equal installments of $$10,000$ each the first of which is a down$-$payment paid to the supplier on January $2,2022.$ Each of the other three payments will be made on December $31$ of the years $2022,2023$ and $2024.$Assuming an implicit interest rate of $10\%,$ the discounted value of the three future payments is $$24,869.$Given the above information, answer the following questions $($in your answer, do not use $"$$$"$ nor $"\%"$ signs and give answers rounded to the nearest dollar.$)$

The value of the machine to be recorded in the books on January $2,2022$ is