Five years ago you took out a $\frac{5}{1}$ adjustable rate mortgage and the five$-$year fixed rate period has just expired. The loan was originally for $$306,000$ with $360$ payments at $4\mathrm{.}1\%$ 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 $0\mathrm{.}9\%,$ to $5\%$ APR, compounded monthly, what will be your new payments?

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

The remaining balance on the loan is $ $($Round to the nearest cent.$)$