$($Continuous compounding, $11)$ Suppose you have $$1$ million and you can invest it in a bank account that pays interests at an annual percentage rate $($APR$)$ of $5\%.$ You want to invest your $$1$m for $3$ years. $($a$).$ Suppose you are allowed to reinvest the interest at the end of every year $($i$.$e$.,$ annual compounding$).$ What is the balance of your account at the end of year $3?(2)($b$).$ Suppose you are allowed to reinvest the interest at the end of every month $($i$.$e$.,$ monthly compounding$).$ What is the balance of your account at the end of year $3?(2)($c$).$ Suppose you are allowed to reinvest the interest at the end of every day $($i$.$e$.,$ daily compounding$).$ What is the balance of your account at the end of year $3?($Assume there are $365$ days in a year.$)(2)($d$).$ Suppose you are allowed to reinvest the interest at the end of every hour $($i$.$e$.,$ hourly compounding$).$ What is the balance of your account at the end of year $3?($Assume there are $365$ days in a year and $24$ hours in a day.$)(2\backslash$