Find the mortgage balance after the first three payments on a $20-$year $$170,000$ mortgage that was financed at an APR of $4\mathrm{.}25\%$ and has a monthly payment of $$1052\mathrm{.}70.$

Payment Number Interest Payment Principal Payment Mortgage Balance

$1$ $$602\mathrm{.}08$ $$450\mathrm{.}62$ Balance $1$

$2$ $$600\mathrm{.}49$ $$452\mathrm{.}21$ Balance $2$

$3$ $$598\mathrm{.}89$ $$453\mathrm{.}81$ Balance $3$