During the fourteen years he ran it$,$ an investment firm's CEO reportedly earned an annual rate of return of over $100$ percent, potentially turning an initial investment of $$1$ milion into more than $$11$ million by the time he left in $1990.$

a$.$ What rate of return, compounded annually, would turn $$1$ million into $$11$ million by $1990?$

b$.$ The actual rate of return during the fourteen years the CEO ran the investment firm was $113\%.$ How much would $$1$ million, compounded annually, be worth after $14$ years?

a$.$ A rate of return of $\%$ would turn $$1$ million into $$11$ million.

$($Do not round until the final answer. Then round to the nearest hundredth as needed.