$4.$ Sandra stopped working, and stopped contributing to the Canada Pension Plan, on her $65$th birthday. At age $65,$ she applied for and began to receive her CPP retirement income. Her birthday falls on July $1$st$,1957.$ She has worked in Canada since the age of $18.$ Her total

adjusted pensionable earnings $($TAPE$)$ and her adjusted TAPE are $$1,634,691\mathrm{.}14$ and $$1,470,151\mathrm{.}43,$ respectively.

a$.$ What is her CPP retirement pension?

b$.$ If her benefits are approved immediately after she applies, for how many months will she receive retroactive payments?

c$.$ On January $1$st$,2023,$ Sandra returned to the workforce for one year. She will earn an annual income of $$40,000.$ What is her monthly PRB for $2024?$