A city has two sources to borrow $$200,000.$ The first source is to borrow at j$1=9\%$ and amortize the debt for $10$ years with annual payments of $$31,164.$ For the second source, the money can be borrowed at j$1=8\%$ if the interest is paid annually and the principal is repaid in a lump sum at the end of $10$ years. Assume that a sinking fund can earn money at j$1=$ x$\%.$ Find x$.$