Bob plans to deposit a total of $$12,000$ each year for $9$ years, either by quarter or by year. He has two choices.

Option $1$: he deposits $$12,000$ once per year at an annual rate of $x\%$ compounded annually

Option $2$: he deposits $$3,000$ each quarter at an annual rate of $y\%$ compounded quarterly

You can assume that $x$ is larger than $y.$

Which option does he prefer?

The option with the highest future value

Option $1$ because the interest rate is higher

Option $2$ because his funds compound quarterly

We cannot compare these options because one compounds quarterly and one annually