Suppose you found your dream house and you intend to buy it with a $$197,705,16-$year, $5\%$ APR mortgage with a $7\%$ annual payment cap $($meaning monthly will not rise beyond $7\%$ of last year's monthly payment$).$ If the interest rate climes by $2\%$ next year, what will be the loan balance at the end of the $2$ nd year?