The following paragraph applies to questions $9-10.$

You have a new client that inherited an Andy Warhol painting from her grandmother at the beginning of $2024.$ Your client's grandmother purchased the piece for $$1,000$ at the beginning of $1970$ from a family friend. Your research has led you to find that similar pieces were sold at auction at the beginning of $1985$ for $$18,000$ and the beginning of $2007$ for $$82,000.$ Other similar pieces experienced similar price trends. Your client finds a buyer for the art piece because the painting doesn't fit the style of her home. The buyer and your client agree to a $5\%$ price increase from the beginning of $2024$ value and will be sold $366$ days after the inheritance date.

$9.$ Using the repeat sales method, what is the value of your client's art upon inheritance at beginning of $2024($show your work$)?$

$10.$ How much capital gains will your client pay based on the sale $($show your work$)?$