Ms$.$ Esperanto obtained a $$41,500$ home equity loan at $8\mathrm{.}9\%$ compounded monthly. $($Do not round intermediate calculations. Round the PMT and final answers to $2$ decimal places.$)$

a$.$ What will she pay monthly if the amortization period is $12$ years?

Payment $

per month

b$.$ How much of the payment made at the end of the fifth year will go towards principal and how much will go towards interest?

Principal $

Interest $

c$.$ What will be the balance on the loan after five years?

Balance $

d$.$ How much interest did she pay during the fifth year?

Interest paid $