For Problems $9-14,$ pretend you receive an inheritance of $$650,000$ and deposit it in a savings plan that earns $5\mathrm{.}25\%$ compounded monthly.

$9.$ If you want to live off the interest without withdrawing any of the $$650,000$ principal, what amount can you withdraw at the end of each month?

$10.$ How much can you withdraw at the end of each month if you want the plan to last $35$ years?

$11.$ How much can you withdraw at the end of each month if you want the plan to last $50$ years?

$12.$ If you withdraw $$4,550$ at the end of each month, how long will the plan last?

$13.$ If you withdraw less than the amount you calculated in Problem $9,$ what will happen to the plan balance?

$14.$ If you withdraw $$2,800$ at the end of each month, what will the balance be in $30$ years?