A bank proudly announces that it has changed its interest computation method to continuous compounding now $2000

Question:

A bank proudly announces that it has changed its interest computation method to continuous now $2000 left in the bank for 9 years will double to $4000.
(a) What nominal interest rate, compounded continuously, is the bank paying?
(b) What effective interest rate is it paying?
Compounding
Compounding is the process in which an asset's earnings, from either capital gains or interest, are reinvested to generate additional earnings over time. This growth, calculated using exponential functions, occurs because the investment will...