I am having trouble understanding the solution and why I keep getting a diffirent answer. here it is
I am confused about why the '$Y$' in the time line are above 5 and 6.when it says she pays back at the end of the fifth year and end of sixth year, doesn't this imply that the $Y$ should be over the $6$ and over the $7$?
Because then I get Y=$10170$
So can anyone help me understand what I am missing?

I guess it is just notation: look where the 8500 is places: it is bellow zero, meaning that we consider that person x lends person y 8500 at the beginning of year one (so the end of year 0). Therefore thé Y are above 5 and 6.