Athena took out a home loan $5$ years ago with a $30-$year term, monthly payments of $$2100,$ and an interest rate of $5\%/$year compounded monthly on the unpaid balance. She is looking to refinance with a $3\mathrm{.}75\%$ per year interest rate and a $25-$year loan term.

a$)$ Find the outstanding principal after $5$ years of regular payments.

b$)$ What would the new monthly payment be$?$

Use units and context for both answers. Round answers to two decimal places.