Your bank account pays interest with an effective annual interest rate $($EAR$)$ of $10\%.$

$($a$)$ If you invest $$1000$ now, how much do you receive in one year?

$($b$)$ What is the percentage return per annum based on semiannual compounding?

$($c$)$ What is the percentage return per annum based on monthly compounding?

$($d$)$ What is the continuously compounded annual interest rate?

$($e$)$ Suppose you want to have $$500000$ saved by the time you reach age $30$ and suppose that you are $20$ years old today. How much would you have to invest today to reach your goal?