I plan to retire in $15$ years from today $01/01/2024.$

I have $$50,000$ in a savings account which will earn $5\mathrm{.}15\%$ interest per annum compounding monthly.

From today I will deposit $$3000\mathrm{.}00$ at the end of each month into the savings account.

I estimate I will need to have a lump sum of $$1,200,000$ in $15$ years to live comfortable for the next $20$ years.

I want to invest with a different investment bank, which has an average return of $14\%$ per annum, compounding monthly. With a brokerage fee of $4\%$ commission per annum.

$1.$ How long would it take to save $$1,200,000?($show workings$).$ Would it be within my $15$ year time frame? $($show workings$).$

$2.$ Assume I save $$1,200,000$ in $15$ years. At retirement my interest rate changes to $5\mathrm{.}15\%$ per annum, compounding annually. How much would I be able to withdraw each year for $20$ years of retirement? $($show workings$).$

$3.$ What is the effective annual return from an interest rate of $14\%$ per annum, compounding monthly, with a brokerage fee of $4\%$ commission? $($show workings$).$