Suppose you found your dream house and you intend to buy it with a $$220,106,21-$year, $8\%$ APR mortgage with a $6\%$ annual payment cap $($meaning monthly will not rise beyond $6\%$ of last year's monthly payment$).$ If the interest rate climes by $0\mathrm{.}7\%$ next year, what will be the loan balance at the end of the $2$ nd year?