Consider a variable rate mortgage for $$100,000$ with a $300-$month amortization period, and with a nominal semiannual rate of $5\%$ at loan origination. Suppose that the rate is held constant for the first $12$ monthly payments. Then in month $13($so affecting the $13$th payment$)$ and for the remainder of the loan's life, the rate on the loan falls to a nominal semiannual rate of $2\%.$ If the payment is held constant $($at the initial payment for month $1),$ what will be the balance after the $14$th payment?