$(5$ Marks$)$ A bank pays $4\%$ compounded annually. At the end of $4$ years, a $2\%$ bonus is paid on the balance. If $$1000$ is invested for $4$ years, what is the effective annual rate of

interest earned by the investor? Plz answer it nicely using the formualas nicely from the chapter compound interest!! Plz be clear with the work!!