Federal Housing Administration $($FHA$)$ provides graduated payment mortgages for homebuyers who currently have low to moderate incomes but expect them to increase substantially over the next $5$ to $10$ years. One of the plans provided by the FHA is such that the payments increase by $5\%$ annually in the first $5$ years of the loan, and stays constant thereafter at the year $5$ level till its maturity in year $30.$ The mortgage is fully amortized $($no ballon payment at the end$).$ If the contractual interest rate is $6\%$ APR, what are the annual payments in years $1-10?$ What is the outstanding loan balance at the end of the $5$th year? Assume that the outstanding loan balance at origination is $$250,000$ and payments are made at the end of each year.