As a retirement plan, you would like to have an annual income of $$60,000$ forever. Assume a savings account with a $7\%$ interest rate compounded monthly.

a$.$ How much principal do you need in order to withdraw $$60,000$ per year forever at a $7\%$ interest rate?

b$.$ What monthly payment into this account will be required in order to obtain this amount $($answer to part a$)$ in $30$ years