The George's would like to save for their $10$ year old daughter's college education. They are using the in$-$state cost $($tuition$,$ fees, and room & board$)$ of UNC$-$Chapel Hill as an estimate for savings. Currently it costs $$27,500$ per year and will likely increase $4\mathrm{.}5\%$ annually. Investment returns for moderate portfolios are about $7\%$ annually.

They anticipate their daughter to take a gap year as many are doing these days. If their daughter enrolls in UNC$-$CH at $19$ years old, what will the first year cost? Round your answer to the nearest hundred using conventional rounding rules, and do not use commas or dollar signs. Ex: If the answer is $$10,567\mathrm{.}32,$ enter $10600$