Professor$$s Annuity Corporation offers a lifetime annuity to retiring professors. For a payment of $$80,000$ at age $65,$ the firm will pay the retiring professor $$600$ a month until his death.

If the professor$$s remaining life expectancy is $20$ 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.

What is the effective annual interest rate?

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

If the monthly interest rate is $\mathrm{.}5\%,$ what monthly annuity payment can the firm offer to the retiring professor?