A loan of $$40,000$ is to be amortized in $12$ level annual payments. The interest rate for the first $4$ years is $4\%,$ the interest rate for the next $4$ years $($years $5$ to $8)$ is $5\%,$ while the interest rate for the last $4$ years of the loan is $6\%.$ Calculate the loan balance after the $6$ th payment. Show all work please. Not on excel