An existing mortgage has interest rate of $7\mathrm{.}30\%,$ fixed monthly payments, remaining term of $22$ years, and current balance of $$160,600.$ If the refinancing cost is $4\%$ of the outstanding mortgage balance, what interest rate on a new fixed$-$rate $22-$year loan will result in the implied annual savings rate of $10\%$ assuming that the loan is not to be prepaid until the end of its term?