A $30$ year adjustable rate mortgage $($ARM$)$ offers a $2$ year teaser rate of $2\%.$ After which, the rate starts at $4\mathrm{.}5\%,$ then adjusts based on actual interest rates. The max rate is $10\mathrm{.}5\%,$ but the rate cannot increase by more than $200$ bps a year. Consider a mortgage for $$250,000.$

$-1^{st}$ year payment?

$2^{nd}$ year payment?

Max $3^{rd}$ year payment?

Max $4^{th}$ year payment?