Professor's Annuity Corporation offers a lifetime annuity to retiring professors. For a payment of $$87,000$ at age $65,$ the firm will pay

the retiring professor $$775$ a month until his death.

a$.$ If the professor's remaining life expectancy is $15$ years, what is the monthly interest rate on this annuity?

Note: Do not round intermediate calculations. Enter your answer as a percent rounded to $2$ decimal places.

b$.$ What is the effective annual interest rate?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

c$.$ If the monthly interest rate is $0\mathrm{.}75\%,$ what monthly annuity payment can the firm offer to the retiring professor?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.