Five years$$ ago, you took out a$5/1$ adjustable rate mortgage and the $5-$year fixed rate period has just expired. The loan was originally for $$$$303$ comma $000$ with $360$ payments at $4\mathrm{.}2\%$APR$,$ compounded monthly.

a$.$ Now that you have made $60$payments$,$ what is the remaining balance on the$$ loan?

b$.$ If the interest rate increases by $1\mathrm{.}1\%,$ to $5\mathrm{.}3\%$APR$,$ compounded$$ monthly, what will be your new$$ payments?