Sandra figures that her budget allows her to spend up to $$2,900\mathrm{.}00$ on her monthly mortgage payment. Her bank offers a $3\mathrm{.}375\%$ amortized loan for $40$ years.

a$)$ What is the maximum amount she can borrow from the bank for a mortgage? Round to the nearest cent.

b$)$ How much will she end up paying in interest? Round to the nearest cent.